Invited Session 09：量子概率与信息

49

组织者：骆顺龙,中国科学院数学与系统科学研究院

Gaussian states as minimum uncertainty states

Shuangshuang Fu, 傅双双

University of Science and Technology Beijing shuangshuang.fu@ustb.edu.cn

Abstract

Gaussian distributions and Gaussian states are fundamental and ubiquitous in

probability theory and quantum theory. In bosonic fields, Gaussian states constitute a rather

wide family of states including coherent states, squeezed states, thermal states, etc., and have

many classical-like features, which are usually defined from the mathematical perspective in

terms of characteristic functions. It is well known that some special Gaussian states, such as

coherent states, are minimum uncertainty states for the conventional Heisenberg uncertainty

relation involving canonical pair of position and momentum observables. A natural question

arises as whether all Gaussian states can be characterized as minimum uncertainty states. In

this work, we show that indeed Gaussian states coincide with minimum uncertainty states for

an information-theoretic refinement of the conventional uncertainty relation. This

characterization puts Gaussian states on a novel basis of physical significance.

From asymmetry to correlations

Nan Li, 李楠

AMSS, Chinese Academy of Sciences linan@amss.ac.cn

Abstract

Symmetry, as well as the dual concept of asymmetry, are essential, powerful and

ubiquitous in physics and nature. Motivated by the original Wigner-Yanase skew information

and its extension by Dyson (Wigner E. P. and Yanase M. M., Proc. Natl. Acad. Sci. U.S.A.,

49 (1963) 910), which quantifies the information content of a quantum state skew to a

conserved observable and may be reinterpreted as asymmetry of a state with respect to an

observable, we address the issue of quantifying asymmetry and symmetry of states with

respect to Lie groups and Lie algebras. We elucidate that correlations arise naturally from the

difference between asymmetries of global and local states. This provides a fundamental

insight into correlations. The idea is further illustrated by several examples.

Invited Session 09：量子概率与信息

50

The uncertainty of quantum channels in terms of variance

Yuan Sun, 孙源

Nanjing Normal University sunyuan@njnu.edu.cn

Abstract

By use of the generalized variance for any operator (not necessarily Hermitian), we

introduce the uncertainty of quantum channels as the sum of the generalized variances for

the Kraus operators of quantum channels and prove that it satisfies several desirable

properties. Then we establish two trade-off relations between the uncertainty of quantum

channels and the entanglement fidelity which is introduced by Schumacher [Phys. Rev. A 54,

2614 (1996)] and quantifies how well the channel preserves the entanglement between the

input system and the auxiliary system for purification. Finally, we illustrate the uncertainty

of quantum channels through some typical examples.

Probability density functions of uncertainties of observables

Lin Zhang, 张林

Hangzhou Dianzi University godyalin@163.com

Abstract

We consider the uncertainties, as quantified by the standard deviation (square root of

variance), of quantum observables in random states. We analytically derive the probability

density functions (PDFs) of the uncertainties of qubit observables. Based on these PDFs, we

can characterize uncertainty regions of observables as the supports of such PDFs. Moreover,

we transform the state-independent uncertainty relations into the optimization problems over

uncertainty regions. This opens a new vista for studying uncertainty relations in a more

detailed and analytical way. These results may be generalized to multiple observables in

higher dimensional spaces.

Invited Session 10：离散概率模型及其尺度极限

51

组织者：李欣意, 北京大学

Heat kernel on the infinite percolation cluster

Chenlin Gu, 顾陈琳

New York University Shanghai guchenlin@hotmail.com

Abstract

The central limit theorem (CLT) is one of the most important results in probability, and

it has many generalizations in random processes and other stochastic models. In the last

decades, the heat kernel estimate on percolation cluster and other random conductance

models have been largely studied and many results of CLT type are obtained. In this talk, I

will review these results and present a new heat kernel estimate obtained in collaboration

with Paul Dario.

Movement of Lee-Yang zeros

Jianping Jiang, 姜建平

Tsinghua University jianpingjiang@tsinghua.edu.cn

Abstract

For the Ising model with ferromagnetic pair interactions and a uniform complex external

field, we consider the zeros of its partition function. In this talk, we discuss the movement of

those zeros as the underlying interactions are varied. Based on joint work with Federico

Camia, Qi Hou and Charles M. Newman.

Invited Session 10：离散概率模型及其尺度极限

52

A heterogeneous spatial model in which savanna

and forest coexist in a stable equilibrium

Ruibo Ma, 马瑞博

Beijing Jiaotong University rbma@bjtu.edu.cn

Abstract

In work with a variety of co-authors, Staver and Levin have argued that savanna and

forest coexist as alternative stable states with discontinuous changes in density of trees at the

boundary. Here we formulate a nonhomogeneous spatial model of the competition between

forest and savanna. We prove that coexistence occurs for a time that is exponential in the size

of the system, and that after an initial transient, boundaries between the alternative equilibria

remain stable.

Directed polymers in random environments

Jinjiong Yu, 俞锦炯

East China Normal University jjyu@sfs.ecnu.edu.cn

Abstract

An (1 + ?)-dimensional directed polymer is a random walk under the associated Gibbs

measure generated together with random environments, where the environment region is

ℕ × ℤ

d

. When the random environment region is degenerated to ℕ × {0}, the model is also

known as the disordered pinning model. We study an interpolation of these two models,

namely the region grows polynomially along with time, which we call a directed polymer in

tube. We will review recent results for all these models, regarding the phase transitions among

disorder relevance, marginal relevance and disorder irrelevance. Joint work with Ran Wei.

Invited Session 11：生命科学中的随机数学理论

53

组织者： 贾晨，北京计算科学研究中心

单细胞随机基因表达动力学的数学理论

Chen Jia, 贾晨

Beijing Computational Science Research Center chenjia@csrc.ac.cn

Abstract

许多重要的细胞过程都基于基因调控，因此揭示基因表达的动力学机制对于理解

基本的细胞功能是极端重要的。然而，由于基因表达是一个复杂的生化过程，对其建

立合理的生物数学模型，并由此解释最新的实验现象是一项极具挑战性的任务，相关

研究是计算系统生物学的热点与前沿。我将结合我与合作者的最新研究成果，简要介

绍基因表达系统的数学建模与数学理论，希望能起到抛砖引玉的作用。

Coalescent process and its applications in population history inference

Xumin Ni, 倪旭敏

Beijing Jiaotong University xmni@bjtu.edu.cn

Abstract

The coalescent process is a powerful modeling tool in population genetics. In this talk,

we will introduce some basic ideas of the coalescent theory and our IBD-based migration

history inference method. Under the population model with migration, we propose a

framework to estimate identity by descent (IBD) sharing, which is a very important genomic

feature in population genetics and can be used to reconstruct recent demographic history. We

adopt the structured coalescent theory and use a continuous-time Markov jump process to

describe the genealogical process. Then we apply Kolmogorov backward equation to

calculate the distribution of coalescence time and develop a formula to estimate the IBD

sharing. The simulation studies demonstrate that our method is robust and accurate.

Invited Session 11：生命科学中的随机数学理论

54

Monte Carlo simulations of stochastic L-V competition models

Fengying Wei, 魏凤英

Fuzhou University weifengying@fzu.edu.cn

Abstract

The well-known stochastic Lotka-Volterra model for interacting multi-species in

ecology has some typical features: highly nonlinear, positive solution and multi-dimensional.

The known numerical methods including the tamed/truncated Euler-Maruyama (EM) applied

to it do not preserve its positivity. The aim of this talk is to modify the truncated EM to

establish a new positive preserving truncated EM (PPTEM). To simplify the proof as well as

to make our theory more understandable, we will first develop a nonnegative preserving

truncated EM (NPTEM) and then establish the PPTEM. Of course, we should point out that

the NPTEM has its own right as many SDE models in applications have their nonnegative

solutions. This is a joint work with Xuerong Mao and Teerapot Wiriyakraikul.

Hydrodynamics of an epidemic model in linear systems

Xiaofeng Xue, 薛晓峰

Beijing Jiaotong University xfxue@btju.edu.cn

Abstract

In this talk we are concerned with the hydrodynamic limit of the binary contact path

process, which is a linear system describing the spread of an epidemic on the lattice ℤ

?

. In

this model, when a vertex ? is infected by a neighbor ?, then the seriousness ?(?) of the

ill at ? is added with that of ?. We show that, when the infection rate ? and dimension ?

are sufficiently large, the hydrodynamic limit of the process is driven by a heat equation and

the fluctuation from the above hydrodynamic limit is driven by a measure-valued O-U

process. This talk is based on joint works with Dr. Linjie Zhao.

Invited Session 12：随机矩阵

55

组织者：鲍志刚, 香港科技大学

Phase transition of eigenvalues in non-Hermitian

random matrix theory

Dangzheng Liu, 刘党政

University of Science and Technology of China dzliu@ustc.edu.cn

Abstract

Consider a random matrix of size ? as an additive deformation of the complex Ginibre

ensemble under a deterministic matrix ?0 with a finite rank, independent of ?. When some

eigenvalues of ?0 separate from the unit disk, outlier eigenvalues may appear asymptotically

in the same locations, and their fluctuations exhibit surprising phenomena that highly depend

on the Jordan canonical form of ?0. These findings are largely due to Benaych-Georges and

Rochet, Bordenave and Capitaine, and Tao. When all eigenvalues of ?0 lie inside the unit

disk, we prove that local eigenvalue statistics at the spectral edge form a new class of

determinantal point processes, for which correlation kernels are characterized in terms of the

repeated erfc integrals. This thus completes a non-Hermitian analogue of the BBP phase

transition in Random Matrix Theory. Duality formulae between different random matrix

ensembles play a key role. This talk is based on joint work with Lu Zhang (USTC),

arXiv:2204.13171v2.

双正交（biorthogonal）多项式渐近分析的 Riemann-Hilbert 方法

Dong Wang, 王东

University of Chinese Academy of Sciences wangdong@wangd-math.xyz

Abstract

由联合分布密度

1

1

( )( ( ) ( )) ( ) i j i j i i

i j n

x x f x f x w x

=

  

 − − 

给出的? -粒子系统称为

双正交系综（bi-orthogonal ensemble），因为它与双正交多项式有密切联系。（如果

?(?) = ?，则他退化为与权函数?(?)相联系的系综。）本报告以两种具体的双正交多

项式为例，我们讨论一个比较通用的，求解双正交多项式的 Plancherel-Rotach 渐近的

方法。我们的方法是通过把双正交多项式转化为一个向量 Riemann-Hilbert 问题，然后

用 Deift-周方法求渐近。这是求解正交多项式渐近性质的 Riemann-Hilbert 方法的推广。

Invited Session 12：随机矩阵

56

Limiting distribution for extreme eigenvalues of

large Fisher matrices with divergent numbers of spikes

Junshan Xie, 解俊山

Henan University junshan@henu.edu.cn

Abstract

Consider the ? × ? matrix that is the product of a population covariance matrix and the

inverse of another population covariance matrix. Suppose that their difference has a divergent

rank with respect to ?, when two samples of sizes ? and ? from the two populations are

available, we construct its corresponding sample version. In the regime of high dimension

where both ? and ? are proportional to ? , weinvestigate the limiting laws for extreme

(spiked) eigenvalues of the sample (spiked) Fisher matrix when the number of spikes is

divergent and these spikes are unbounded. This is a jointed work with Yicheng Zeng and

Lixing Zhu.

Gap probability near the cusp singularity

in random matrix ensembles

Shuaixia Xu, 徐帅侠

Sun Yat-sen University xushx3@mail.sysu.edu.cn

Abstract

In this talk, we study the gap probability of finding no eigenvalues in an interval near

the cusp singularity in random matrix ensembles. It is known that the cusp singularity leads

to a new universal determinantal process characterized by the Pearcey kernel. By studying

the Pearcey-kernel determinant, we establish an integral representation of the gap probability

in terms of the Hamiltonian associated with a family of special solutions to a system of

nonlinear differential equations. Together with some remarkable differential identities for the

Hamiltonian, this allows us to obtain the asymptotics of the gap probability as the size of the

interval tends to infinity. This talk is based on joint work with Dan Dai and Lun Zhang.

Invited Session 13：随机（偏）微分方程及应用

57

组织者：林一青, 上海交通大学

Spatial and temporal white noises under sublinear ?-expectation

Xiaojun Ji, 纪晓君

Shandong University jixj@sdu.edu.cn

Abstract

In this talk, we introduce a new type of ?-Gaussian random fields under the framework

of sublinear expectation, which contains one type of spatial white noise as a special case.

Based on that, we further introduce a spatial-temporal ? -white noise and develop the

corresponding stochastic calculus with respect to the spatial and spatial-temporal white

noises. Unlike the regular case under the linear expectation, spatial ?-white noises are now

intrinsically different from temporal ones accounting for the uncertainty of probability

measures.

A type of globally solvable BSDEs with triangularly

quadratic generators

Peng Luo, 罗鹏

Shanghai Jiao Tong University peng.luo@sjtu.edu.cn

Abstract

The present paper is devoted to the study of the well-posedness of a type of BSDEs with

triangularly quadratic generators. This work is motivated by the recent results obtained by

Hu and Tang [14] and Xing and Zitkovic [28]. By the contraction mapping argument, we first

prove that this type of triangularly quadratic BSDEs admits a unique local solution on a small

time interval whenever the terminal value is bounded. Under additional assumptions, we

build the global solution on the whole time interval by stitching local solutions. Finally, we

give solvability results when the generators have path dependence in value process.

Invited Session 13：随机（偏）微分方程及应用

58

A study of backward stochastic differential equation

on a Riemannian manifold

Wenjie Ye, 叶文杰

AMSS, Chinese Academy of Sciences yewenjie@amss.ac.cn

Abstract

Suppose N is a compact Riemannian manifold, in this talk we will introduce the

definition of N-valued BSDEs and L

2

(?

m;N)-valued BSDEs for which the solutions are

not necessarily staying in only one local coordinate. Moreover, the global existence of a

solution to L

2

(?

m;N)-valued BSDEs will be proved without any convexity condition on N.

?-moment estimate for the singular ?-Laplace equation

and applications

Liming Yin, 殷礼鸣

Shanghai Jiao Tong University gacktkaga@sjtu.edu.cn

Abstract

p-laplace equations are an important class of parabolic equations which arise to model

natural nonlinear diffusion phenomenon such as groundwater infiltration. These equations

are well studied, yet some quantitative behavior of solutions such as q -moment and

convergence rate with respect to Wasserstein metric are still not fully studied.

In this talk, we focus on the Cauchy problems of singular p-laplace equation with initial

data Radon measure and present q-moment estimates on annuli and q-uniform integrability

for its weak solutions for some critical parameter range. As applications, we derive a mass

conservation as well as a weak convergence result for the whole fast diffusion range of

parameter. Concerning the latter point, we further study the rate of convergence of the

solution with respect to q-Wasserstein metric. This talk is based on joint work with Prof.

Samuel Drapeau.

Invited Session 14：随机分析及其应用

59

组织者：刘伟，武汉大学

On the entropy power inequality and related topics

Xiangdong Li, 李向东

AMSS, Chinese Academy of Sciences xdli@amt.ac.cn

Abstract

In 1948, Claude Shannon established the mathematical foundation of information

theory. In his classical paper, Shannon discovered the entropy power inequality. Since

then, this inequality has received a lot of attentions in information theory, probability theory,

convex geometry, differential geometry and related topics. In this talk, I will briefly recall

the classical form of the entropy power inequality and its two proofs, then I will present its

connection with probability theory, convex geometry and differential geometry. Finally, I will

present our recent work on the entropy power inequality and the optimal transport problem,

which leads to a new understanding to Lott-Villani and Sturm’s synthetic geometry on the

curvature-dimension condition on metric measure spaces.

Some new results on probabilities of moderate deviations

for i.i.d. random variables

Yu Miao, 苗雨

Henan Normal University yumiao728@gmail.com

Abstract

Let {?, ??; ? ≥ 1} be a sequence of independent and identically distributed random

variables and set ?? = ?ⅈ=1

? ?ⅈ

, ? ≥ 1. In this paper, we give some new results on

probabilities of moderate deviations for Sn. From these results, we can see that, unlike those

known results in the literature, the moderate deviation results established in this paper depend

on both the variance and the asymptotic behavior of the tail distribution of ?. The talk is

based on joint works with Deli Li and Yongcheng Qi.

Invited Session 14：随机分析及其应用

60

Sinkhorn barycenter via functional gradient descent

Zhenfu Wang, 王振富

Peking University zwang@bicmr.pku.edu.cn

Abstract

We consider the problem of computing the barycenter of a set of probability distributions

under the Sinkhorn divergence. This problem has recently found applications across various

domains, including graphics, learning, and vision, as it provides a meaningful mechanism to

aggregate knowledge. Unlike previous approaches which directly operate in the space of

probability measures, we recast the Sinkhorn barycenter problem as an instance of

unconstrained functional optimization and develop a novel functional gradient descent

method named Sinkhorn Descent (SD). We prove that SD converges to a stationary point at

a sublinear rate, and under reasonable assumptions, we further show that it asymptotically

finds a global minimizer of the Sinkhorn barycenter problem. Moreover, by providing a

mean-field analysis, we show that SD preserves the weak convergence of empirical measures.

Importantly, the computational complexity of SD scales linearly in the dimension d and we

demonstrate its scalability by solving a 100-dimensional Sinkhorn barycenter problem. This

is a joint work with Zebang Shen, Alejandro Ribeiro and Hamed Hassani from UPenn.

The kinetic Fokker-Planck equation with mean field interaction

Chaoen Zhang, 张朝恩

Harbin Institute of Technology chaoenzhang@hit.edu.cn

Abstract

In this talk we will present our results on the long time behavior of the kinetic FokkerPlanck equation with mean field interaction (of which the limit is often called Vlasov-FokkerPlanck equation). We prove a uniform (in the number of particles) exponential convergence

to equilibrium for the solutions in the weighted Sobolev space with a rate of convergence

which is explicitly computable and independent of the number of particles. The originality

of the proof relies on functional inequalities and hypocoercivity with Lyapunov type

conditions, usually not suitable to provide adimensional results. Based on joint works with

Arnaud Guillin, Wei Liu and Liming Wu.

Invited Session 15：随机分析

61

组织者：刘伟，江苏师范大学

McKean-Vlasov SDEs and SPDEs with locally monotone coefficients

Wei Hong, 洪伟

Tianjin University weihong@tju.edu.cn

Abstract

In this talk we mainly investigate the strong and weak well-posedness of a class of

McKean-Vlasov stochastic (partial) differential equations. The main existence and

uniqueness results state that we only need to impose some local assumptions on the

coefficients, i.e. locally monotone condition both in state variable and distribution variable,

which cause some essential difficulty since the coefficients of McKean-Vlasov stochastic

equations typically are nonlocal. The wide applications of main results are illustrated by

various concrete examples such as the Granular media equations, Kinetic equations,

distribution dependent porous media equations and Navier-Stokes equations, moreover, we

could remove or relax some typical assumptions previously imposed on those models.

SPDEs with gradient driven by space-time fractional noises

Yiming Jiang, 江一鸣

Nankai University ymjiangnk@nankai.edu.cn

Abstract

We study a class of SPDEs driven by space-time fractional noises, where we suppose

that the drift term contain a gradient and satisfies certain conditions. We prove the existence

and uniqueness and joint Hölder continuity on the solution to the SPDEs.

Invited Session 15：随机分析

62

Averaging principle for multi-scale SDEs driven by Lévy processes

Xiaobin Sun, 孙晓斌

Jiangsu Normal University xbsun@jsnu.edu.cn

Abstract

In this talk, we will present some recent results about the averaging principle for multiscale SDEs driven by Lévy processes. More precisely, we establish the optimal strong and

weak convergence orders for such kind of multi-scale stochastic system under the

monotonicity condition. The obtained results can applied to a class of multi-scale SDEs with

polynomial growth coefficients. This is a joint work with Yinghui Shi, Liqiong Wang and

Yingchao Xie.

Stochastic nonlinear Schrödinger equation

driven by pure jump noise

Jiahui Zhu, 朱佳惠

Zhejiang University of Technology jiahuizhu@zjut.edu.cn

Abstract

In this talk, we consider the stochastic nonlinear Schrödinger equation with

multiplicative jump noise in the Marcus canonical form. We establish a version of the

stochastic Strichartz estimate for stochastic convolution driven by jump noise and prove the

existence and uniqueness of a global solution to stochastic nonlinear Schrödinger equation

with either focusing or defocusing nonlinearity in the full subcritical range of exponents.

Invited Session 16：随机偏微分方程

63

组织者：罗德军,中国科学院数学与系统科学研究院

Well-posedness and wave-breaking for the stochastic

rotation-two-component Camassa-Holm system

Hongjun Gao, 高洪俊

Southeast University hjgao@seu.edu.cn

Abstract

We study the global well-posedness and wave-breaking phenomenon for the stochastic

rotation-two-component Camassa-Holm (R2CH) system. First, we find a Hamiltonian

structure of the R2CH system and use the stochastic Hamiltonian to derive the stochastic

R2CH system. Then, we establish the local well-posedness of the stochastic R2CH system

by the dispersion-dissipation approximation system and the regularization method. We also

show a precise blow-up criterion for the stochastic R2CH system. Moreover, we prove the

global existence of the stochastic R2CH system occurs with high probability. At last, we

consider transport noise case and establish the local well-posedness and another blow-up

criterion.

Well-posedness of stochastic partial differential equations

with fully local monotone coefficients

Shijie Shang, 尚世界

University of Science and Technology of China sjshang@ustc.edu.cn

Abstract

Considered in a Gelfand triple, the well-posedness of stochastic partial differential

equations with monotone or particular type of local monotone coefficients is now well

understood.

In this talk, we will report recent progresses on the well-posedness of stochastic partial

differential equations which have fully local monotone coefficients. The results apply to

many interesting models/examples. This is a joint work with Michael Röckner and Tusheng

Zhang.

Invited Session 16：随机偏微分方程

64

Stochastic transport equation with bounded and Dini continuous drift

Jinlong Wei, 魏金龙

Zhongnan University of Economics and Law weijinlong@zuel.edu.cn

Abstract

For stochastic transport equations with bounded and Dini continuous drift, by using the

Itô-Tanaka trick we prove the uniqueness of L

∞ -solutions, which generalizes Flandoli,

Gubinelli and Priola's result (Invent. Math. 180 (2010) 1-53) for bounded and Hölder

continuous drift. Moreover, we obtain the existence and uniqueness of stochastic quasidiffeomorphisms flows for a stochastic differential equation with the drift in the same class.

Multi-bubble blow-up solutions and multi-solitons

to (stochastic) nonlinear Schrödinger equations

Deng Zhang, 张登

Shanghai Jiao Tong University dzhang@sjtu.edu.cn

Abstract

In this talk we are mainly concerned with the dynamics of a general class of focusing

mass-critical nonlinear Schrödinger equations (NLS) with lower order perturbations, for

which the pseudo-conformal symmetry and the conservation law of energy can be absent.

Two canonical examples are stochastic NLS driven by linear multiplicative noise and

deterministic NLS. We show the construction of multi-bubble Bourgain-Wang type blow-up

solutions, and the uniqueness in the energy class where the convergence rate is of the order

(T − t)

4+ . In the case of mass-critical NLS, the corresponding existence and conditional

uniqueness of non-pure multi-solitons (including dispersive part) also will be presented.

These results in particular provide new examples of mass quantization conjecture and soliton

resolution conjecture. If time permits, I will also show the recent results on the refined

uniqueness of multi-bubble blow-ups and multi-solitons for the mass-critical NLS, and the

pathwise construction of multi-solitons for the mass-subcritical stochastic NLS.

Invited Session 17：保险数学

65

组织者：柏立华，南开大学

S-shaped narrow framing, skewness and the demand for insurance

Yichun Chi, 池义春

Central University of Finance and Economics yichun@cufe.edu.cn

Abstract

The existing literature in insurance economics has shown that narrow framing can

explain why people buy too little insurance compared to what standard theory predicts.

However, there is also ample evidence suggesting people sometimes buy too much insurance.

In this talk, we assume S-shaped narrow framing, i.e., the local utility function for evaluating

the net insurance payoff is convex in the loss domain but concave in the gain domain, and

show that it can reconcile with both insurance puzzles simultaneously. Especially, we show

the policyholder under S-shaped narrow framing is more likely to underinsure more

negatively skewed risks of loss but to overinsure less negatively skewed risks of loss. We

further characterize the optimal insurance scheme under S-shaped narrow framing while

incentive compatibility is satisfied. It contains a straight deductible when the net insurance

payoff is negative but partial insurance when the net insurance payoff is positive. (This is a

joint work with Jiakun Zheng and Sheng Chao Zhuang).

De Finetti’s optimal dividend under Chapter 11 bankruptcy

Wenyuan Wang, 王文元

Xiamen University wwywang@xmu.edu.cn

Abstract

Motivated by recent developments in risk management based on the U.S. bankruptcy

code, in this paper we revisit De Finetti optimal dividend problems by incorporating the

reorganization process and regulator's intervention documented in Chapter 11 bankruptcy.

The resulting surplus process, bearing financial stress towards the more subtle concept of

bankruptcy, corresponds to non-standard spectrally negative Lévy processes with endogenous

regime switching. In both models without and with fixed transaction costs, some explicit

expressions of the expected net present values under a barrier strategy, new to the literature,

are established in terms of scale functions. With the help of these expressions, when the tail

of the Lévy measure is log-convex, the optimal dividend control in each problem is verified

to be of the barrier type and the associated optimal barrier can be obtained in analytical form.

(This is a joint work with Xiang Yu at Department of Applied Mathematics, The Hong Kong

Polytechnic University and Xiaowen Zhou at Department of Mathematics and Statistics,

Concordia University)

Invited Session 17：保险数学

66

Mean-variance portfolio selection with stochastic dominance constraints

Jiaqin Wei, 危佳钦

East China Normal University jqwei@stat.ecnu.edu.cn

Abstract

This paper is concerned with a mean-variance portfolio selection problem with first and

second order stochastic dominance constraints in complete markets. First, a variance

minimizing problem is solved by Lagrangian multipliers in its quantile formulation. Then,

the mean-variance efficient frontier with stochastic dominance constraints is derived by

studying a global variance minimizing problem. Moreover, closed-form solution can be

obtained in a special case and numerical solution is provided by the projected gradient

method.

Valuation of variable annuities with guaranteed minimum maturity

benefits and periodic fees

Zhimin Zhang, 张志民

Chongqing University zmzhang@cqu.edu.cn

Abstract

We consider the valuation of variable annuities with guaranteed minimum maturity

benefits on a set of predetermined discrete tenor dates under a regime-switching Levy model.

The policyholder can choose surrender the policy at any discrete time points before maturity

and receive a surrender benefit. In addition, we consider a periodic fee structure, namely, fees

are deducted at some proportion from the policyholder's account according to whether the

policyholder's account value at discrete time point is greater or less than a pre-specified level.

Under the assumption of the periodic fee structure, we derive the values and the optimal

surrender strategies of the constant guarantee and cliquet-style guarantee embedded in

variable annuity contracts by Fourier cosine series expansion method. Numerical results are

provided to confirm the accuracy and efficiency of the method.

Invited Session 18：随机环境下的马氏过程

67

组织者：邵井海，天津大学

Delay feedback control for switching diffusion systems

Xiaoyue Li, 李晓月

Northeast Normal University lixy209@nenu.edu.cn

Abstract

For the sake of saving time and costs the feedback control based on discrete-time

observations is used to stabilize the switching diffusion systems. Response lags are required

by most of physical systems and play a key role in the feedback control. The aim of this paper

is to design delay feedback control functions based on the discrete-time observations of the

system states and the Markovian states in order for the controlled switching diffusion system

(SDS) to be exponentially stable in pth moment and probability one as well as stable in H∞.

The designed control principles are implementable to stablize quasi-linear and highly

nonlinear SDSs. For quasi-linear SDSs the criteria are sharp that under the control with high

strength the controlled SDSs will be stable (bounded) while under the weaker control they

will be unstable (unbounded) in mean square. The sample and moment Lyapunov exponents

are estimated which have close relationship with the time delays.

Long time behavior of Lévy-driven Ornstein-Uhlenbeck process

with regime-switching

Zhongwei Liao, 廖仲威

Beijing Normal University zhwliao@bnu.edu.cn

Abstract

In this work we investigate the long time behavior of the Ornstein-Uhlenbeck process

driven by Lévy noise with regime-switching. We provide explicit criteria on the transience

and recurrence of this process. Contrasted with the Ornstein-Uhlenbeck process driven

simply by Brownian motion, whose stationary distribution must be light-tailed, both the

jumps caused by the Lévy noise and regime-switching described by Markov chain can derive

the heavy-tailed property of the stationary distribution. In this work, the different role played

by Lévy measure and regime-switching process is clearly characterized.

Invited Session 18：随机环境下的马氏过程

68

Estimates for general decay rates for a class of Markov

switching diffusion processes

Lingdi Wang, 王玲娣

Henan University wangld_2013@163.com

Abstract

We focus on the almost surely stable with a general decay rate for a class of Markov

switching diffusion processes in the paper. By using principal eigenvalue methods, some

sufficient conditions and quantitative estimates of the rate for the almost surely stable of the

process are obtained. A kind of examples are investigated carefully.

Regime-switching diffusion processes with infinite delay

Fubao Xi, 席福宝

Beijing Institute of Technology xifb@bit.edu.cn

Abstract

In this work we consider a class of regime-switching diffusion processes, which are

determined by solutions X(t) to stochastic functional differential equation with infinite

delay and random switching represented by jump process Λ(t) . We first establish the

existence and uniqueness of the underlying process by an interlacing procedure. Under

suitable conditions, we then investigate convergence and boundedness of both the solutions

X(t) and the functional solutions X?

. We show that two solutions (resp. functional solutions)

from different initial data living in the same initial switching regime will be close with high

probability as time variable tends to infinity, and that the solutions (resp. functional solutions)

are uniformly are bounded in the mean square sense. Moreover, we prove existence and

uniqueness of the invariant probability measure of two-component Markov-Feller process

(X?

, Λ(t)) , and establish exponential bounds on the rate of convergence to the invariant

probability measure under Wasserstein distance. Finally, we provide a concrete example to

illustrate our main results.

Invited Session 19：随机偏微分方程

69

组织者：宋健，山东大学

Nonlinear fractional stochastic heat equation

with Gaussian noise rough in space

Junfeng Liu, 刘俊峰

Nanjing Audit University junfengliu@nau.edu.cn

Abstract

In this talk we consider a class of nonlinear fractional stochastic heat equation

?

?? ?(?, ?) = ??

??(?, ?) + ?(?(?, ?))?̇ (?, ?), (?, ?) ∈ [0, ?] × ℝ ,

in (1 + 1)-dimension with T > 0, where ??

?

is a nonlocal fractional differential operator

with ? ∈ (1,2) and |?| ≤ 2 − ?. The diffusion coefficient ?(·) is a measurable function.

?̇ is a Gaussian noise which is white in time and behaves as a fractional Brownian motion

with Hurst index H satisfying (3 − ?)/4 ≤ ? ≤ 1/2 in the space variable. Under some

mild assumptions, we prove the existence and uniqueness of the mild solution in some

function spaces. Along the way, we study the moment bounds for the solution and show that

the solution is weakly full intermittent.

CLT for SPDEs

Fei Pu, 蒲飞

Beijing Normal University fei.pu@bnu.edu.cn

Abstract

I will present some recent progress on the central limit theorem for stochastic partial

differential equations. This is based on collaborations with Le Chen, Davar Khoshnevisan,

Zenghu Li and David Nualart.

Invited Session 19：随机偏微分方程

70

Bismut formula for intrinsic/Lions derivatives of distribution dependent

SDEs with singular coefficients

Yulin Song, 宋玉林

Nanjing University songyl@amss.ac.cn

Abstract

By using distribution dependent Zvonkin's transforms and Malliavin calculus, the

Bismut type formula is derived for the intrinisc/Lions derivatives of distribution dependent

SDEs with singular drifts, which generalizes the corresponding results derived for classical

SDEs and regular distribution dependent SDEs. This is joint work with Xing Huang and

Feng-Yu Wang.

Dean-Kawasaki equation with singular non-local interactions

Rangrang Zhang, 张让让

Beijing Institute of Technology rrzhang@bit.edu.cn

Abstract

This paper is concerned with Dean-Kawasaki equation with non-local singular

interaction and correlated noise, which describes the evolution of the density function for a

system of finitely many particles governed by Langevin dynamics. Due to the presence of

non-local interaction term, the noise taking the form of a stochastic conservation law and the

lack of Lipschitz continuity of the noise, the well-posedness and large deviations are proved

in the framework of renormalized stochastic kinetic solution.

Invited Session 20：非线性期望

71

组织者：宋永生，中国科学院数学与系统科学研究院

Limit theorems for pseudo-independent random variables

on sublinear expectation space

Xinpeng Li, 李欣鹏

Shandong University lixinpeng@sdu.edu.cn

Abstract

We establish the law of large numbers and law of the iterated logarithm for pseudoindependent random variables on sublinear expectation space. The counterexamples for the

law of large numbers and law of the iterated logarithm are also provided, which raise some

new problems which are exclusive on sublinear expectation space.

Stopping times and related topics under nonlinear expectation

Guomin Liu, 刘国民

Nankai University gmliu@nankai.edu.cn

Abstract

Stopping time is one of the most important concepts in the classical stochastic analysis.

Whereas under the nonlinear G -expectation, due to the complexity of the representation

probability family, the stopping times tend to be irregular and the analysis on them becomes

a subtle problem. In this talk, we shall present some fundamental properties on stopping times

under the nonlinear expectation framework, including the quasi-continuity properties of exit

times for nonlinear semimartingales, the random-time conditional expectations and the strong

Markov property for stochastic differential equations driven by G-Brownian motion.

Invited Session 20：非线性期望

72

Linear regression under model uncertainty

Shuzhen Yang, 杨淑振

Shandong University yangsz@sdu.edu.cn

Abstract

We consider a classical linear regression model where the model is subject to two types

of uncertainty: given covariates are responsible for one part of the response variable while

the remaining part has no clearly defined form, and the variance of error is also undetermined

and may change randomly according to a mechanism unknown to the statistician. By

following the recent theory of sublinear expectation, we propose to characterize such mean

uncertainty and variance uncertainty by two specific nonlinear random variables: these

nonlinear random variables in fact encompass an infinite family of probability distributions

in the sense of (linear) classical probability theory. Joint work with Jianfeng Yao.

Parabolic path-dependent master equation and ?-expectation

Huilin Zhang, 张会林

Shandong University huilinzhang@sdu.edu.cn

Abstract

Master equations are PDEs for measure-dependent unknowns, and are introduced to

describe asymptotic equilibrium of large scale mean-field interacting systems, especially in

games and control theory. In this talk we introduce new semilinear master equations whose

unknowns are functionals of both paths and path measures. They include state-dependent

master equations, path-dependent partial differential equations (PPDEs), history information

dependent master equations and time inconsistent (e.g. time-delayed) equations, which

naturally arise in stochastic control theory and games. We give a classical solution to the

master equation by introducing a new notation called strong vertical derivative (SVD) for

path-dependent functionals, inspired by Dupire's vertical derivative, and applying stochastic

forward-backward system argument. Moreover, we consider a general non-smooth case with

a functional mollifying method. In the end, we will point out further development through

?-expectation.

Invited Session 21：Lévy 跳过程的应用

73

组织者：王健，福建师范大学

Existence of invariant measures for functional McKean-Vlasov SDEs

Jianhai Bao, 鲍建海

Tianjin University jianhaibao@tju.edu.cn

Abstract

In this talk, we show existence of an invariant probability measure for a class of

functional McKean-Vlasov SDEs by applying Kakutani's fixed point theorem to a suitable

class of probability measures on a space of continuous functions. With contrast to the existing

literature, we do not assume a monotonicity condition to hold. Further, our conditions are

even weaker than some results in the literature on invariant measures for functional SDEs

without dependence on the law of the solution.

Quantification of stochastic homogenization

for stable-like random walk

Xin Chen, 陈昕

Shanghai Jiao Tong University chenxin217@sjtu.edu.cn

Abstract

We will prove the speed of convergence for the solutions of scaled elliptic equations

associated with stable-like random walk in a random conductance model, whose jumping

kernel may be degenerate. The talk is based on an on-going work with Zhen-qing Chen,

Takashi Kumagai and Jian Wang.

Invited Session 21：Lévy 跳过程的应用

74

Regularity of transition densities for affine jump-diffusion processes

Peng Jin, 金鹏

BNU-HKBU United International College pengjin@uic.edu.cn

Abstract

Affine processes are Markov processes for which the logarithm of the characteristic

function of its transition distribution ??

(?,·) is affine with respect to the initial state x .

Affine processes have found a wide range of applications in finance, due to their

computational tractability and modeling flexibility. Many popular models in finance, such as

the models of Cox et al., Heston and Vasicek, are of affine type. A systematic treatment of

affine processes was given in the seminal work of Duffie, Filipovic and Schachermayer. In

this talk I will present our recent results on the transition density for an affine process on the

canonical state space ℝ≥0

? × ℝ?

. Under a Hörmander-type condition for diffusion

components as well as a boundary non-attainment assumption, we derive the existence and

regularity of the transition density for the affine process and then prove the strong Feller

property. Moreover, we also show that under these and the additional subcritical conditions

the corresponding affine process on the canonical state space is exponentially ergodic in the

total variation distance. This talk is based on a joint work with Martin Friesen, Jonas Kremer

and Barbara Rüdiger.

Continuous-state branching processes with immigration and competition

Peisen Li, 李培森

Beijing Institute of Technology peisenli@bit.edu.cn

Abstract

Continuous-state branching processes with immigration and competition are

constructed as pathwise unique solutions of stochastic integral equations driven by Brownian

motions and Poisson random measures. We establish the conditions for extinction and coming

down from infinity. We also present precise conditions on the competition term, for the

exponential ergodicities in both the Wasserstein and the total variation distances.

Invited Session 22：极限理论

75

组织者： 胡治水， 中国科学技术大学

Self-normalized Cram?́r type moderate deviations

for martingales with applications

Xiequan Fan, 范协铨

Tianjin University fanxiequan@hotmail.com

Abstract

Let (?ⅈ

,ℱⅈ)ⅈ≥1 be a sequence of martingale differences. Set ?? = ∑ ?ⅈ

?

ⅈ=1

and

[?]? = ∑ ?ⅈ

? 2

ⅈ=1

. In this talk, we will introduce some Cramer type moderate deviation

expansions for ?(??/√[?]? ≥ ?) as ? → ∞. The results partly extend the classical work

of (Jing, Shao and Wang, 2003, Ann. Probab.) for independent random variables.

Applications to $t$-statistic and stationary sequences are also discussed. This talk is based

on join work of Quansheng LIU, Ion GRAMA and Qi-Man SHAO.

An enhanced strong invariance principle for the elephant random walk

Qunqiang Feng, 冯群强

University of Science and Technology of China fengqq@ustc.edu.cn

Abstract

The elephant random walk (ERW) is a discrete-time random walk on ℤ with a memory

about the whole past. It has been shown that the asymptotic behavior of the ERW depends

heavily on a memory parameter 0 ≤ ? ≤ 1. In this work, we establish the strong invariance

principle for the ERW in the diffusive regime 0 ≤ ? < 3/4 and the critical regime ? = 3/4,

which enhances the known results in Coletti, Gava and Sch?̈tz (2017). This is a joint work

with Hu Zhishui.

Invited Session 22：极限理论

76

The first exit time of fractional brownian motion

Dawei Lu, 鲁大伟

Dalian University of Technology dwlu@dlut.edu.cn

Abstract

Consider a fractional Brownian motion starting at an interior point of the minimum and

maximum parabolic domains, Let ??ⅈ? and ???? denote the first times that the fractional

Brownian motion exits from ??ⅈ? and ???? , respectively. Asymptotically equivalent

estimates of ??? ?(??ⅈ? > ?) and ??? ?(???? > ?) are respectively given by using

Gordon's inequality, depending on the relationship between ?1 and ?2. The proof methods

are based on early works of Li, Shi, Lifshits, Aurzada and Lu.

Limit theorems for linear processes under sub-linear expectation

Yong Zhang, 张勇

Jilin University zyong2661@jlu.edu.cn

Abstract

In this talk, the limit theorems for linear processes are obtained under sub-linear

expectation, including central limit theorem, moderate deviation, law of iterated logarithm.

This talk is based on a joint work with Doctor Wei Liu.

Invited Session 23：随机微分方程

77

组织者：巫静, 中山大学

One-dimensional diffusion and stochastic differential equation

Wenjie Sun, 孙文杰

Tongji University wjsun@tongji.edu.cn

Abstract

In this talk, we study the condition for a one-dimensional diffusion to satisfy a stochastic

differential equation. In the case of regular diffusion, we give a suffcient and necessary

condition using scale function and speed measure. For general diffusions, we decompose the

state space into regular and shunt pieces, and give a condition for diffusion satisfying a

stochastic differential equation on any shunt pieces.

Asymptotic behavior of the second derivative of self-intersection local

time of Brownian motion

Xianye Yu, 余显烨

Zhejiang Gongshang University xianyeyu@gmail.com

Abstract

In this talk, we establish the central limit theorem of the ?-th chaotic component of

second derivative of self-intersection local time w.r.t Brownian motion by the Wiener chaos.

By product, we give an answer to a conjecture of Markowsky.

Invited Session 23：随机微分方程

78

Regularity of the density for the stochastic heat equations with jumps

Hua Zhang, 张华

Jiangxi University of Finance and Economics zh860801@163.com

Abstract

In this paper, the smoothness of the density of the solution to the nonlinear stochastic

heat equation with jumps is established using the lent particle method created by Bouleau

and Denis.

On stochastic functional variational inequalities

Jing Wu, 巫静

Sun Yat-sen University jjosie@hotmail.com

Abstract

In this talk, we study stochastic functional variational inequalities. Weak and strong

solutions under appropriate conditions are established for this type of equations. Properties

of the solution process, including Markov property, stability, and ergodicity are also discussed.

Invited Session 24：极限理论及其应用

79

组织者：徐礼虎, 澳门大学

Nonzero-sum risk-sensitive average stochastic games

Xian Chen, 陈娴

Xiamen University chenxian@xmu.edu.cn

Abstract

We study discrete-time nonzero-sum stochastic games under the risk-sensitive average

cost criterion. The state space is a denumerable set, the action spaces of players are Borel

spaces, and the cost functions are unbounded. Under suitable conditions, we first introduce

the risk-sensitive first passage payoff functions and obtain their properties. Then, we establish

the existence of a solution to the risk-sensitive average cost optimality equation of each player

for the case of unbounded cost functions and show the existence of a randomized stationary

Nash equilibrium in the class of randomized history-dependent strategies. This is a joint work

with Qingda Wei.

Poisson equation on Wasserstein space and diffusion

approximations for McKean-Vlasov equation

Longjie Xie, 解龙杰

Jiangsu Normal University longjiexie@jsnu.edu.cn

Abstract

We consider the fully-coupled McKean-Vlasov equation with multi-time-scale

potentials, and all the coefficients depend on the distributions of both the slow component

and the fast motion. By studying the smoothness of the solution of the non-linear Poisson

equation on Wasserstein space, we derive the asymptotic limit as well as the optimal rate of

convergence for the slow process. Extra homogenized drift term containing derivative in the

measure argument of the solution of the Poisson equation appears in the limit, which seems

to be new and is unique for systems involving the fast distribution. This is based on a joint

work with Y. Li and F. Wu.

Invited Session 24：极限理论及其应用

80

Complexity of high dimensional Gaussian random

fields with isotropic increments

Qiang Zeng, 曾强

University of Macau qiangzeng@um.edu.mo

Abstract

The number of critical points of a random function is a basic question and is commonly

called complexity. The notion of random fields with isotropic increments was introduced by

Kolmogorov in the 1940s. In 2004, Fyodorov computed the large N limit (on the exponential

scale) of expected number of critical points for isotropic Gaussian random fields. However,

many natural models are not isotropic and only have isotropic increments, which creates new

difficulty in understanding the complexity. In this talk, I will present some results on the large

N behavior of complexity of non-isotropic Gaussian random fields with isotropic increments.

Connection to random matrices and large deviations will be explained. This talk is based on

joint work with Antonio Auffinger (Northwestern University).

On geometries of finitary random interlacements

Yuan Zhang, 张原

Peking University zhangyuan@math.pku.edu.cn

Abstract

In this talk, we discuss geometric properties of Finitary Random Interlacements (FRI)

ℱℐ

?,?

in ℤ

?

. We prove that with probability one ℱℐ

?,?

has no infinite connected

component for all sufficiently small fiber length ? > 0, and a unique infinite connected

component for all sufficiently large ?. At the same time, although FRI may not enjoy global

stochastic monotonicity with respect to ?, we prove the existence of a critical ??(?) for all

large ?. Moreover, we find the chemical distance on the infinite cluster is of the same order

as Euclidean distance as well as a local uniqueness result for all sufficiently large ?.

Researches joint with E.B. Procaccia, J. Ye, Y. Xiong, Z. Cai, and X. Han.

Invited Session 25：风险管理与优化

81

组织者：徐玉红, 苏州大学

Centralized systemic risk control in the interbank system:

relaxed control and Gamma-convergence

Lijun Bo, 薄立军

Xidian University lijunbo@xidian.edu.cn

Abstract

This talk discusses a systemic risk control problem by the central bank, which

dynamically plans monetary supply for the interbank system with borrowing and lending

activities. Facing both heterogeneity among banks and the common noise, the central bank

aims to find an optimal strategy to minimize the average distance between log-monetary

reserves and some prescribed capital levels for all banks. A relaxed control approach is

adopted, and an optimal randomized control can be obtained in the system with finite banks

by applying Ekeland’s variational principle. As the number of banks grows large, we further

prove the convergence of optimal strategies using the Gamma-convergence arguments, which

yields an optimal relaxed control in the mean field model. It is shown that the limiting optimal

relaxed control is linked to a solution of a stochastic Fokker-Planck-Kolmogorov (FPK)

equation. The uniqueness of the solution to the stochastic FPK equation is also established

under some mild conditions.

Computations of the stochastic control problems

from finance and insurance

Jingtang Ma, 马敬堂

Southwestern University of Finance and Economics mjt@swufe.edu.cn

Abstract

In this talk, I will present two classes of numerical methods for solving the stochastic

control problems (or HJB equations/variational inequalities) arising in finance and insurance.

The first one is the finite difference method (FDM) with iteration policy for solving the HJB

equations and variational inequalities arising in regime switching optimal investment. The

second one is the delta family approach for the two-dimensional stochastic control (and

stopping) problems from the optimal investment and reinsurance-investment, including the

case under the classical and rough Heston stochastic volatility models, and stochastic local

volatility models such as the stochastic alpha beta rho (SABR) models. The convergence for

the first one is obtained, while not for the second one, although it is relatively easier to

implement. This talk is based on the recent joint work with Zhenyu Cui (Stevens Institute of

Technology), Zhengyang Lu, Jianjun Ma and Haofei Wu (SWUFE).

Invited Session 25：风险管理与优化

82

Pricing fair premium for MBS in a CDO under

a reduced form credit risk model with regime switching

Guojing Wang, 王过京

Soochow University gjwang@suda.edu.cn

Abstract

We introduce a homogeneous portfolio reduced form credit risk model with regime

switching to describe the default behaviors for the mortgage holders. We can use the

occupation times of Markov chain to express the default loss and the fair premium for the

loss of the different tranche investors in the CDO. We use the Markov property and the

uniformization method for Markov chain to derive some explicit formulas for the

distributions of those occupation times. Basing on these results, we obtain some explicit

expressions for the default loss and its fair premium. We also present some numerical results

to illustrate the influence of the model parameters on the default loss and the fair premium.

(This talk is based on a joint work with Professor S.N. Chiu and Dr. G. Wang).

G-VaR and its application to risk management

Yuhong Xu, 徐玉红

Soochow University yhxu@suda.edu.cn

Abstract

G-VaR, which is a type of worst-case value-at-risk (VaR), is defined as measuring risk

incorporating model uncertainty. Compared with most extant notions of worst-case VaR, GVaR can be computed using an explicit formula, and can be applied to large portfolios of

several hundred dimensions with low computational cost. We also apply G-VaR to robust

portfolio optimization, thereby providing a tractable means to facilitate optimal allocations

under the condition of market ambiguity.

Invited Session 26：金融数学与保险

83

组织者：许左权，香港理工大学

The (un)importance of small jumps in Lévy model option pricing

Xuecan Cui, 崔雪璨

Southwestern University of Finance and Economics cuixc@swufe.edu.cn

Abstract

Option pricing literature argues that the behaviour of small jumps in a Geometric Lévy

model is of paramount importance [1]. This is evidently true for very short time horizons and

very deep in- and out-of-the-money options. In this paper, we take the complementary view

and ask what values of time to maturity and option moneyness in a Geometric Lévy model

lead to option prices that are practically indistinguishable from the price of plain vanilla

options in the Black-Scholes model. In other words, when can the Lévy model in question be

replaced with a Brownian motion with minimal pricing error? We produce explicit tight

bounds in the case of a Poisson jump process and related heuristic bounds for arbitrary Lévy

process with exponentially decaying jump intensity. We test the latter for tempered stable

process of [2].

REFERENCES

[1] Svetlana I. Boyarchenko and Sergei Z. Levendorskii. Non-Gaussian Merton-Black

Scholes Theory. World Scientific, 2002.

[2] Peter Carr, Hélyette Geman, Dilip B. Madan, and Marc Yor. The fine structure of asset

returns: An empirical investigation. Journal of Business, 75:305-332, 2002.

Multivariate copula-dependent distortion risk measures

Yijun Hu, 胡亦钧

Wuhan University yjhu.math@whu.edu.cn

Abstract

In this talk, we will introduce two new classes of multivariate risk measures, which are

referred to as multivariate copula-dependent distortion risk measures. We define and

axiomatically characterize the class of multivariate scalar copula-dependent distortion risk

measures through the tool of multivariate Choquet integral. As a by-product, this

characterization can also be regarded as a multivariate extension of the univariate Greco's

Representation Theorem. Furthermore, based on the representations for the multivariate

scalar copula-dependent distortion risk measures, we will introduce the class of multivariate

Invited Session 26：金融数学与保险

84

vector-valued copula-dependent distortion risk measures, and their properties of copuladependent monotonicity, translation invariance, positive homogeneity and pi-comonotone

additivity are shown. Finally, we present several examples, among which one example

introduces a new class of vector-valued risk measures, while the others demonstrate the

comparisons of the introduced multivariate vector-valued distortion risk measures with those

vector-valued risk measures known as in the literature. This talk is based on a joint work with

Suo Gong and Linxiao Wei.

A survey on backward stochastic Volterra integral equations

Tianxiao Wang, 王天啸

Sichuan University wtxiao2014@scu.edu.cn

Abstract

In this talk, I will give a survey on the theory of backward stochastic Volterra integral

equations, as well as their applications in partial differential equations, stochastic optimal

controls problem, mathematical finance.

Dynamic optimal reinsurance and dividend-payout

in finite time horizon

Zuoquan Xu, 许左权

The Hong Kong Polytechnic University maxu@polyu.edu.hk

Abstract

This paper studies a dynamic optimal reinsurance and dividend-payout problem for an

insurer in a finite time horizon. The goal of the insurer is to maximize its expected cumulative

discounted dividend payouts until bankruptcy or maturity which comes earlier. The insurer

is allowed to dynamically choose reinsurance contracts over the whole time horizon. This is

a mixed singular-classical control problem and the corresponding Hamilton-Jacobi-Bellman

equation is avariational inequality with fully nonlinear operator and with gradient constraint.

The ?

1,2

smoothness of the value function and a comparison principle for its gradient

function are established by penalty approximation method. We find that the surplus-time

space can be divided into three non-overlapping regions by a risk-magnitude-and-timedependent reinsurance barrier and a time-dependent dividend-payout barrier. The insurer

should be exposed to higher risk as surplus increases; exposed to all the risks once surplus

upward crosses the reinsurance barrier; and pay out all reserves in excess of the dividendpayout barrier. The localities of these regions are explicitly estimated.

Invited Session 27：跳过程及大偏差

85

组织者：翟建梁，中国科学技术大学

Hörmander's hypoelliptic theorem for nonlocal operators

Xuhui Peng, 彭旭辉

Hunan Normal University xhpeng@hunnu.edu.cn

Abstract

We show the Hörmander hypoelliptic theorem for nonlocal operators by a purely

probabilistic method: the Malliavin calculus. Roughly speaking, under general Hörmander's

Lie bracket conditions, we show the regularization effect of discontinuous Lévy noises for

possibly degenerate stochastic differential equations with jumps. To treat the large jumps, we

use the perturbation argument together with interpolation techniques and some short time

asymptotic estimates of the semigroup. This work is based on joint work with Zimo Hao and

Xicheng Zhang.

Large deviations for DMZ equation driven by Lévy noise

Jie Xiong, 熊捷

Southern University of Science and Technology xiongj@sustech.edu.cn

Abstract

In this talk, we focus on the asymptotic behavior of the optimal filter where both signal

and observation processes are driven by Lévy noises. Indeed, we study large deviations for

the DMZ equation, which is an SPDE satisfied by the unnormalized filter, in the case that the

signal-to-noise ratio is small. Weak convergence approach will be taken. To that end, we first

prove the uniqueness of the solution of the controlled Duncan-Mortenson-Zakai and

Kushner-Stratonovich equations. For this, we employ a method which transforms the

associated equations into SDEs in an appropriate Hilbert space. Next, taking into account the

controlled analogue of Zakai and Kushner-Stratonovich equations, respectively, the large

deviation principle follows by employing the existence, uniqueness and tightness of the

solutions. This talk is based on a paper joint with Maroulas and Pan.

Invited Session 27：跳过程及大偏差

86

Existence and pathwise uniqueness to an SPDE

driven by ?-stable colored noise

Xu Yang, 杨叙

North Minzu University xuyang@mail.bnu.edu.cn

Abstract

In this talk we study a stochastic partial differential equation (SPDE) with Hölder

continuous coefficient driven by an α-stable colored noise. The pathwise uniqueness is

proved by using a backward doubly stochastic differential equation backward (SDE) to take

care of the Laplacian. The existence of solution is shown by considering the weak limit of a

sequence of SDE system which is obtained by replacing the Laplacian operator in the SPDE

by its discrete version. This talk is based on a joint work with Jie Xiong.

Regularity of 3D stochastic Burgers equation

Guoli Zhou, 周国立

Chongqing University zhouguoli736@126.com

Abstract

By utilising the so-called Doss-Sussman transformation, we link our stochastic 3D

Burgers equation with linear multiplicative noise to a random 3D Burger equation. With the

help of techniques from partial differential equations (PDEs) and probability, we establish

the global well-posedness of stochastic 3D Burgers with the diffusion coefficient being

constant. Next, by developing a solution which is orthogonal with the gradient of coefficient

of the noise, we extend the global well-posedness to a more general case in which the

diffusion coefficient is spatial dependent, i.e., it is a function of the spatial variable. Finally,

we take advantage of the linear multiplicative noise and the geometrical structure of 3D

stochastic Burgers equation , we establish its’ long-time behavior , which is not observed in

the deterministic case.(Joint work with Zhao Dong and Jianglun Wu)

Invited Session 28：随机系统的分析与控制

87

组织者：张奇，复旦大学

Well-posedness of scalar BSDEs with sub-quadratic generators

and related PDEs

Shengjun Fan, 范胜君

China University of Mining and Technology shengjunfan@cumt.edu.cn

Abstract

We first establish the existence of an unbounded solution to a backward stochastic

differential equation (BSDE) with generator ? allowing a general growth in the state

variable ? and a sub-quadratic growth in the state variable ?, when the terminal condition

satisfies a sub-exponential moment integrability condition, which is weaker than the usual

exp(??) -integrability and stronger than ?

?

( ? >1)-integrability. Then, we prove the

uniqueness and comparison theorem for the unbounded solutions of the preceding BSDEs

under some additional assumptions and establish a general stability result for the unbounded

solutions. Finally, we derive the nonlinear Feynman-Kac formula in this context.

This is a joint work with Prof. Ying Hu (University of Rennes 1).

Optimal controls of stochastic differential equations with jumps

and random coefficients: Stochastic Hamilton-Jacobi-Bellman

with jumps

Qingxin Meng, 孟庆欣

Huzhou university mqx@zjhu.edu.cn

Abstract

In this paper, we study the stochastic HJB equation with jump, which arises from a

corresponding non-Markovian optimal control problem with a recursive utility cost

functional. The solution to the equation is a predictable triplet of random fields (?, Φ, Ψ).

We show that the value function of the control problem, under some regularity assumptions,

is the solution to the stochastic HJB equation; and a classical solution to this equation is the

value function and gives the optimal control. With some additional assumptions on the

coefficients, an existence and uniqueness result in the sense of Sobolev space is shown by

recasting the backward stochastic partial integral differential equation with jumps as a

backward stochastic evolution equation in Hilbert spaces with Poisson jumps.

Invited Session 28：随机系统的分析与控制

88

A Q-learning algorithm for discrete-time linear-quadratic

control with random parameters of unknown distribution

Fu Zhang, 张伏

University of Shanghai for Science and Technology fugarzhang@163.com

Abstract

This talk studies an infinite horizon optimal control problem for discrete-time linear

systems and quadratic criteria, both with random parameters which are independent and

identically distributed with respect to time. A classical approach is to solve an algebraic

Riccati equation that involves mathematical expectations and requires certain statistical

information of the parameters. In this paper, we propose an iterative algorithm in the spirit of

Q-learning for the situation where only one random sample of parameters emerges at each

time step. The first theorem proves the equivalence of three properties: the convergence of

the learning sequence, the well-posedness of the control problem, and the solvability of the

algebraic Riccati equation. The second theorem shows that the adaptive feedback control in

terms of the learning sequence stabilizes the system as long as the control problem is wellposed. Numerical examples are presented to illustrate our results. This is a joint work with

Kai Du and Qingxin Meng.

Quasilinear stochastic PDEs with two obstacles:

probabilistic approach

Jing Zhang, 张静

Fudan University zhang_jing@fudan.edu.cn

Abstract

We prove an existence and uniqueness result for two-obstacle problem for quasilinear

stochastic PDEs (DOSPDEs for short). The method is based on the probabilistic

interpretation of the solution by using the backward doubly stochastic differential equations

(BDSDEs for short). This a joint work with Laurent Denis and Anis Matoussi.

Invited Session 29：时间序列渐近推断理论及其应用

89

组织者：张荣茂，浙江大学

Consistent order selection for ARFIMA processes

Kun Chen, 陈坤

Southwestern University of Finance and Economics chenkun@swufe.edu.cn

Abstract

Estimating the orders of the autoregressive fractionally integrated moving average

(ARFIMA) model has been a long-standing challenge in time series analysis. This paper

tackles the challenge by establishing the consistency of the Bayesian information criterion

(BIC) in ARFIMA models with independent errors. Since we allow the model's memory

parameter to be any unknown real number, our consistency result can apply simultaneously

to short-memory, long-memory, and non-stationary time series. We further extend BIC's

consistency to ARFIMA models with conditional heteroscedastic errors, thereby enhancing

the criterion's range of applications. Finally, the finite-sample implications of our theoretical

results are illustrated using numerical examples.

Efficient importance sampling for copula models

Tianxiao Pang, 庞天晓

Zhejiang University txpang@zju.edu.cn

Abstract

We propose an efficient importance sampling algorithm for rare event simulation under

copula models. The derived optimal probability measure is based on the criterion of

minimizing the variance of the Monte Carlo estimator within a parametric exponential tilting

family. Since copula model is defined on a copula function for one-dimensional marginal

cumulative distribution functions of a random vector, and its moment generating function is

not easy to get, we apply the transform likelihood ratio (TLR) method to have an alternative

exponential tilting family first. And then obtain a simple and explicit expression of the

optimal alternative distribution under this transformed exponential tilting family. The

importance sampling framework we propose is quite general and can be implemented for

many classes of copula models from which sampling is feasible. Monte Carlo simulations

are given to illustrate the theoretical results on finite-sample performance.

Invited Session 29：时间序列渐近推断理论及其应用

90

Gaussian random fields with stationary increments

and their asymptotic properties

Wang Wensheng, 王文胜

Hangzhou Dianzi University wswang@hdu.edu.cn

Abstract

We establish the exact moduli of non-differentiability of Gaussian random fields with

stationary increments. As an application of the result, we prove that the uniform Hö lder

condition for the maximum local times of Gaussian random fields with stationary increments

obtained in Xiao (1997) is optimal. These results are applicable to fractional Riesz-Bessel

processes and stationary Gaussian random fields in the Mat?́rn and Cauchy classes.

Testing alphas in High-dimensional factor pricing models

Qiang Xia, 夏强

South China Agricultural University xiaqiang@scau.edu.cn

Abstract

This paper proposes a new procedure to validate the multi-factor pricing theory by

testing the presence of alpha in linear factor pricing models with a large number of assets.

Because the market's inefficient pricing is likely to occur to a small fraction of exceptional

assets, we develop a testing procedure that is particularly powerful against sparse signals.

Based on the high-dimensional Gaussian approximation theory, we propose a simulationbased approach to approximate the limiting null distribution of the test. Our numerical studies

show that the new procedure achieves substantial power improvement compared to the Wald

type tests under sparse alternatives, and it delivers a more accurate size than the Wald tests

with a power enhancement component.

Invited Session 30：分枝随机游动

91

组织者：何辉, 北京师范大学

The Derrida–Retaux conjecture on recursive models

Xinxing Chen, 陈新兴

Shanghai Jiao Tong University chenxinx@sjtu.edu.cn

Abstract

We are interested in the nearly supercritical regime in a family of max-type recursive

models studied by Derrida and Retaux 2014, and prove that under a suitable integrability

assumption on the initial distribution, the free energy vanishes at the transition with an

essential singularity with exponent 1/2. This gives a weaker answer to a conjecture of Derrida

and Retaux 2014. Other behaviours are obtained when the integrability condition is not

satisfied.

Asymptotic expansions in central limit theorems

for a branching random walk

Zhiqiang Gao, 高志强

Beijing Normal University gaozq@bnu.edu.cn

Abstract

Harris proposed the question on the central limit theorems for a branching random walk

in 1963. Since then, the topic received much attention. Specially, in 1994, Revesz started the

research on convergence rates of the central limit theorems for branching random walks

where the migration law is governed by simple random walks or Wiener processes. Chen

(2001) verified Revesz’s conjecture on exact convergence rate. In recent works, we improve

and generalize Chen’s results. Precisely, we improve Chen’s results by deriving further

asymptotic expansions and relaxing the moment conditions on the branching mechanism of

the models therein. Moreover, we extend these results to general cases where the migration

law is governed by random walks on ℝ? or ℤ

?

, as well for branching random walks in

random environments where both the branching mechanism and migration laws vary with

time.

Invited Session 30：分枝随机游动

92

Boundedness of Gaussian processes on trees

Yanqi Qiu, 邱彦奇

Wuhan University yanqi.qiu@hotmail.com

Abstract

We consider a class of homogeneous random weighted sums of Gaussian variables along

rooted geodesic rays in a rooted tree and obtain the necessary and sufficient condition for the

almost sure boundedness of such random sums. The condition obtained is also the necessary

and sufficient condition for the almost sure uniform convergence of random series along all

rooted geodesic rays. This talk is based on a joint work with Yong HAN and Zipeng WANG.

Branching random walks on Hyperbolic spaces

Longmin Wang, 王龙敏

Nankai University wanglm@nankai.edu.cn

Abstract

The branching Brownian motion on the hyperbolic plane with binary fission at rate ? >0

exhibits a phase transition in ?: For ? ≤ 1/8 the number of particles in any compact region

is eventually 0, w.p.1, but for ? > 1/8 the number of particles in any open region grows to

∞ w.p.1. Lalley and Sellke (1987) proved that in the subcritical and critical case (? ≤1/8)

the set ? of all limit points in the boundary circle at ∞ consisting of particle trails is a

Cantor set, while in the supercritical case (? > 1/8) the set Λ has full Lebesgue measure. For

? ≤ 1/8 the Hausdorff dimension of ? is at most 1/2 and has critical exponent 1/2 near the

critical value ?= 1/8. In this talk we will prove the same type of phase transition occurs for

branching random walks on hyperbolic spaces. Based on joint work with Vladas Sidoravicius

and Kainan Xiang.

Invited Session 31：随机过程及其应用

93

组织者：李娟，山东大学

Empirical approximation to invariant measures for mean-field SDE

Kai Du, 杜恺

Fudan University kdu@fudan.edu.cn

Abstract

It is known that a mean-field SDE has a unique invariant probability measure

(stationary distribution) if it satisfies a strong monotonicity condition. In this work, we

introduce a class of path-dependent SDE inspired by control system, and prove that its

empirical measure converges to the invariant measure for the associated mean-field SDE. An

interesting conclusion is that the invariant measures for mean-field SDE may be obtained by

one sample trajectory of a path-dependent SDE. This talk is based on a joint work with Yifan

Jiang.

Relationships between the maximum principle and dynamic

programming for infinite dimensional stochastic control systems

Qi L?̈, 吕琦

Sichuan University lu@scu.edu.cn

Abstract

Pontryagin type maximum principle and Bellman's dynamic programming principle

serve as two of the most important tools in solving optimal control problems. There is a huge

literature on the study of relationship between them. In this talk, we present some results for

the relationships between Pontryagin type maximum principle and dynamic programming

principle for control systems governed by stochastic evolution equations in infinite

dimensional space, with the control variables appearing into both the drift and the diffusion

terms.

Invited Session 31：随机过程及其应用

94

Probabilistic interpretation of a system of coupled

Hamilton-Jacobi-Bellman-Isaacs equations

Qingmeng Wei, 魏庆萌

Northeast Normal University weiqm100@nenu.edu.cn

Abstract

By introducing a stochastic differential game whose dynamics and multi-dimensional

cost functionals form a multi-dimensional coupled forward-backward stochastic differential

equation with jumps, we give a probabilistic interpretation to a system of coupled HamiltonJacobi-Bellman-Isaacs equations. For this, we generalize the definition of the lower value

function initially defined only for deterministic times and states to stopping times and random

variables. The generalization plays a key role in the proof of a strong dynamic programming

principle. This strong dynamic programming principle allows us to show that the lower value

function is a viscosity solution of our system of multi-dimensional coupled Hamilton-JacobiBellman-Isaacs equations. The uniqueness is obtained for a particular but important case.

Optimal dividends with capital injection in the Cram?́r-Lundberg model

Xiaochi Wu, 吴晓驰

Shantou University xchwu@stu.edu.cn

Abstract

We consider a stochastic control problem related to the optimal payment of dividends

in a Cramér-Lundberg-type insurance model with capital injections at a proportional cost.

For claims of general type, a verification result is obtained for the stochastic control problem

following the characterization of its value function as the lowest absolutely continuous supersolution of a convenient Hamilton-Jacobi variational inequality. In particular, we show the

optimality of severity-constrained double barrier policies for the case with exponential claims.

Such strategies consist in paying dividends when the reserve surpasses the upper buffer b and

declaring bankruptcy when the size of the overshoot below zero exceeds the limit ? .

Furthermore, we provide an exhaustive and explicit characterization of optimal doublebarrier strategy via structure equations. Our study results in a dichotomy between cheap and

expensive equity, which consists in a non-trivial generalization of the L∅kka-Zervos phasetransition. Joint work with Florin Avram, Dan Goreac and Juan Li.

第七届全国概率论年会

95

参会人员

序号 姓名 学校 邮箱

1 白天衣 上海纽约大学 tb2848@nyu.edu

2 柏立华 南开大学 lhbai@nankai.edu.cn

3 鲍翮臻 山东大学 baohezhen@qq.com

4 鲍建海 天津大学 jianhaibao@tju.edu.cn

5 鲍志刚 香港科技大学 mazgbao@ust.hk

6 毕俊娜 华东师范大学 jnbi@sfs.ecnu.edu.cn

7 薄立军 西安电子科技大学 lijunbo@xidian.edu.cn

8 蔡格非 北京大学 caigefei1917@pku.edu.cn

9 蔡亮 北京理工大学 cailiang@bit.edu.cn

10 常寅山 四川大学 ychang@scu.edu.cn

11 陈大岳 北京大学 dayue@math.pku.edu.cn

12 陈坤 西南财经大学 chenkun@swufe.edu.cn

13 陈木法 江苏师范大学/北京师范大学 mfchen@bnu.edu.cn

14 陈舒凯 福建师范大学 skchen@mail.bnu.edu.cn

15 陈娴 厦门大学 chenxian@xmu.edu.cn

16 陈晓鹏 汕头大学 xpchen@stu.edu.cn

17 陈昕 上海交通大学 chenxin217@sjtu.edu.cn

18 陈昕昕 北京师范大学 xinxin.chen@bnu.edu.cn

19 陈新兴 上海交通大学 chenxinx@sjtu.edu.cn

20 陈洋 苏州科技大学 chenyang@usts.edu.cn

21 陈增敬 山东大学 zjchen@sdu.edu.cn

22 成灵妍 南京理工大学 cly@njust.edu.cn

23 程兰 湖南第一师范学院 chenglan@hnfnu.edu.cn

24 程梦红 中国矿业大学 3466404015@qq.com

25 池义春 中央财经大学 yichun@cufe.edu.cn

26 崔雪璨 西南财经大学 cuixc@swufe.edu.cn

27 戴洪帅 山东财经大学 mathdsh@gmail.com

28 邓昌松 武汉大学 dengcs@whu.edu.cn

29 丁剑 北京大学 dingjian@math.pku.edu.cn

30 董梁 南京理工大学 DL040@mail.ustc.edu.cn

31 董昭 中国科学院数学与系统科学研究院 dzhao@amt.ac.cn

32 杜恺 复旦大学 kdu@fudan.edu.cn

33 杜乾 河南师范大学 duqian960904@163.com

34 范胜君 中国矿业大学 shengjunfan@cumt.edu.cn

35 范协铨 天津大学 fanxiequan@hotmail.com

第七届全国概率论年会

96

36 方明 厦门大学 mfang@xmu.edu.cn

37 方榕娟 福建师范大学 fangrj@fjnu.edu.cn

38 费涛 集美大学 2955337368@qq.com

39 冯群强 中国科学技术大学 fengqq@ustc.edu.cn

40 冯煜阳 芝加哥大学 alpacayu@pku.edu.cn

41 冯子鑫 武汉大学 FengZiXinFZX@163.com

42 傅双双 北京科技大学 shuangshuang.fu@ustb.edu.cn

43 傅宗奕 山东大学 fuzongyi@sdu.edu.cn

44 高洪俊 东南大学 hjgao@seu.edu.cn

45 高武军 深圳技术大学 gaowujun@sztu.edu.cn

46 高志强 北京师范大学 gaozq@bnu.edu.cn

47 龚光鲁 清华大学 glgong@math.tsinghua.edu.cn

48 龚铄 武汉大学 1113897633@qq.com

49 巩馥洲 中国科学院数学与系统科学研究院 fzgong@amt.ac.cn

50 顾陈琳 上海纽约大学 guchenlin@hotmail.com

51 顾王韫 浙江大学 12135027@zju.edu.cn

52 郭精军 兰州财经大学 guojj@lzufe.edu.cn

53 郭水霞 湖南师范大学 guoshuixia75@163.com

54 郭先平 中山大学 mcsgxp@mail.sysu.edu.cn

55 郭昕 清华大学 guoxin5@sem.tsinghua.edu.cn

56 郭宇辉 山东大学 1052034026@qq.com

57 郭子豪 山东大学 gzhsdu@mail.sdu.edu.cn

58 韩东 上海交通大学 donghan@sjtu.edu.cn

59 韩月才 吉林大学 hanyc@jlu.edu.cn

60 郝晨旭 四川大学 476924193@qq.com

61 郝蕾 山东大学 hao.lei@sdu.edu.cn

62 郝子墨 武汉大学 zimohao@whu.edu.cn

63 何博文 山东大学 hbw@mail.sdu.edu.cn

64 何辉 北京师范大学 hehui@bnu.edu.cn

65 何天成 巴黎高等师范学院 tiancheng.he@ens.psl.eu

66 洪伟 天津大学 weihong@tju.edu.cn

67 洪文明 北京师范大学 wmhong@bnu.edu.cn

68 侯振挺 中南大学 zthou@csu.edu.cn

69 胡明尚 山东大学 humingshang@sdu.edu.cn

70 胡淑兰 中南财经政法大学 hu_shulan@zuel.edu.cn

71 胡亦钧 武汉大学 yjhu.math@whu.edu.cn

72 胡泽春 四川大学 zchu@scu.edu.cn

73 胡治水 中国科学技术大学 huzs@ustc.edu.cn

74 黄琪 山东大学 huangqi_email123@163.com

75 黄逸超 北京理工大学 yichao.huang@outlook.com

第七届全国概率论年会

97

76 霍海峰 广西科技大学 xiaohuo08ok@163.com

77 纪晓君 山东大学 jixj@sdu.edu.cn

78 贾晨 北京计算科学研究中心 chenjia@csrc.ac.cn

79 蹇玲玲 南开大学 janejzh@163.com

80 江龙 中国矿业大学 jianglong365@cumt.edu.cn

81 江一鸣 南开大学 ymjiangnk@nankai.edu.cn

82 姜建平 清华大学 jianpingjiang@tsinghua.edu.cn

83 姜恋姿 山东科技大学 jianglianzi95@163.com

84 姜颖 东北师范大学 2578840216@qq.com

85 蒋为民 山东大学 1377459753@qq.com

86 蒋宇 北京化工大学 2832752368@qq.com

87 金鹏 北京师范大学-香港浸会大学联合国际学院 pengjin@uic.edu.cn

88 荆楷豪 中国科学技术大学 ljm19981231@mail.ustc.edu.cn

89 康凯欣 山东大学 kangkaixin@mail.sdu.edu.cn

90 赖书文 南开大学 875682534@qq.com

91 兰光强 北京化工大学 langq@buct.edu.cn

92 黎怀谦 天津大学 hqlee@amss.ac.cn

93 李博晗 香港中文大学 bohanli@cuhk.edu.hk

94 李楚进 华中科技大学 lichujin@hust.edu.cn

95 李邯武 山东大学 lihanwu@sdu.edu.cn

96 李娟 山东大学 juanli@sdu.edu.cn

97 李俊松 山东大学 jsl_sdu@outlook.com

98 李娜 山东财经大学 naibor@163.com

99 李楠 中国科学院数学与系统科学研究院 linan@amss.ac.cn

100 李培森 北京理工大学 peisenli@bit.edu.cn

101 李钦利 山东大学 1586291607@qq.com

102 李瑞囡 上海对外经贸大学 ruinanli@amss.ac.cn

103 李石虎 江苏师范大学 shihuli@jsnu.edu.cn

104 李宋子 中国人民大学 sli@ruc.edu.cn

105 李翔 浙江大学 12135003@zju.edu.cn

106 李向东 中国科学院数学与系统科学研究院 xdli@amt.ac.cn

107 李晓丹 上海财经大学 xdli15@fudan.edu.cn

108 李晓彤 上海师范大学 x.t.li@foxmail.com

109 李晓月 东北师范大学 lixy209@nenu.edu.cn

110 李欣 科学出版社 lixin_kx@mail.sciencep.com

111 李欣鹏 山东大学 lixinpeng@sdu.edu.cn

112 李欣意 北京大学 xinyili@bicmr.pku.edu.cn

113 李衍伟 山东大学 201916496@mail.sdu.edu.cn

114 李增沪 北京师范大学 lizh@bnu.edu.cn

115 李占新 山东大学 elio_lzx@163.com

第七届全国概率论年会

98

116 李章颂 北京大学 ramblerlzs@pku.edu.cn

117 李真 武汉理工大学 zhenlimath@whut.edu.cn

118 李子腾 河南农业大学 Garfieldteng@163.com

119 李子璇 山东大学 201812064@mail.sdu.edu.cn

120 廉琪琪 河南师范大学 lianqiqi98@163.com

121 梁汉营 同济大学 hyliang@tongji.edu.cn

122 梁新刚 北京工商大学 liangxingang@th.btbu.edu.cn

123 梁渝涛 中科院数学与系统科学研究所 lytmath@pku.edu.cn

124 廖仲威 北京师范大学 zhwliao@bnu.edu.cn

125 林静涛 山东大学 3296588966@qq.com

126 林一青 上海交通大学 yiqing.lin@sjtu.edu.cn

127 林正炎 浙江大学 zlin@zju.edu.cn

128 刘党政 中国科学技术大学 dzliu@ustc.edu.cn

129 刘芳 苏州大学 liuf853@nenu.edu.cn

130 刘国民 南开大学 gmliu@nankai.edu.cn

131 刘国平 华中科技大学 liuguoping@hust.edu.cn

132 刘红 东北师范大学 liuh653@nenu.edu.cn

133 刘佳骏 西交利物浦大学 jiajun.liu@xjtlu.edu.cn

134 刘俊峰 南京审计大学 junfengliu@nau.edu.cn

135 刘琪 北京化工大学 1799839792@qq.com

136 刘润声 北京大学 liurunsheng@pku.edu.cn

137 刘伟 武汉大学 wliu.math@whu.edu.cn

138 刘伟 江苏师范大学 weiliu@jsnu.edu.cn

139 刘扬 浙江工商大学 sukey07828@163.com

140 刘勇 北京大学 "

141 刘昱 北京大学 liuyu8300@stu.pku.edu.cn

142 鲁大伟 大连理工大学 dwlu@dlut.edu.cn

143 陆智超 苏州大学 836670747@qq.com

144 罗德军 中国科学院数学与系统科学研究院 luodj@amss.ac.cn

145 罗鹏 上海交通大学 peng.luo@sjtu.edu.cn

146 骆顺龙 中国科学院数学与系统科学研究院 luosl@amt.ac.cn

147 吕琦 四川大学 lu@scu.edu.cn

148 马恒 北京大学 maheng@stu.pku.edu.cn

149 马敬堂 西南财经大学 mjt@swufe.edu.cn

150 马丽 海南师范大学 malihnsd@163.com

151 马瑞博 北京交通大学 rbma@bjtu.edu.cn

152 马志明 中国科学院数学与系统科学研究院 mazm@amt.ac.cn

153 孟庆欣 湖州师范学院 mqx@zjhu.edu.cn

154 孟维君 中国科学院数学与系统科学研究院 mengwj@amss.ac.cn

155 苗雨 河南师范大学 yumiao728@gmail.com