20180511 ~ 20180513
5月11日（星期五） 

10:00—23:00 
报到—三亚清华数学论坛 

5月12日（星期六） 

08:0008:30 
开幕式 

主持人：向开南 

08:3008:55 
张希承 
Strong Uniqueness of Degenerate SDEs with Sobolev Diffusion coefficients 
08:5509:20 
刘伟 
QuasiLinear SPDE with TimeFractional Derivatives 
09:2009:45 
闫理坦 
Cauchy principal values of some integral functionals driven by a fractional Brownian motion 
09:4510:10 
茶歇 

主持人：张希承 

10:1010:30 
翟建梁 
Wellposed and large deviations for 2D Stochastic NavierStokes equations with jumps 
10:3010:50 
周国立 
Random attractor for the 2D stochastic nematic liquid crystals flows with multiplicative noise 
10:5011:10 
巫静 
On Approximations of the EulerPeano scheme for Multivalued stochastic differential equations 
11:1011:30 
武伟娜 
Stochastic porous media equation on general measure spaces with increasing Lipschitz nonlinearities 
11:3011:50 
黎怀谦 
Largetime behaviors of the heat equation under the generalized curvaturedimension inequality 
12:0014:30 
午餐休息 

主持人：刘伟 

14:3014:55 
李应求 
Application of Poisson approach in occupation times 
14:5515:20 
胡泽春 
随机变量的收敛性和大数定律 
15：2015:45 
向开南 
The first order correction to harmonic measure for random walks of rotationally invariant step distribution 
15:4516:10 
宋永生 
Properties of martingales under sublinear expectations 
16:1016:30 
茶歇 

主持人：胡泽春 

16:3016:50 
毕秀春 
ContinuousTime Portfolio and Consumption Decisions under Loss Aversion 
16:5017:10 
刘党政 
Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles 
17:1017:30 
李利平 
On stiff problems via Dirichlet forms 
17:3017:50 
马春华 
Longterm behaviors of stochastic flows of continuousstate branching processes and extremal processes 
18:0019:00 
晚餐 

5月13日（星期日） 

主持人：闫理坦 

08:0008:25 
金鹏 
Uniqueness in law for stablelike processes of variable order 
08:2508:50 
罗德军 
White noise solution to 2D stochastic Euler equations 
08:5009:15 
邵井海 
Heavy tail and light tail of CoxIngersollRoss processes with regimeswitching 
09:1509:40 
席福宝 
Stabilization of regimeswitching processes by feedback control based on discrete time observations II: statedependent case 
09:4010:00 
茶歇 

主持人：金鹏 

10:0010:20 
张振中 
Ergodicity for SDEs Driven by αStable processes with Markov switching 
10:2010:40 
陈昕 
Functional inequalities on loop space over a general noncompact manifold 
10:4011:00 
胡二彦 
Dirichlet heat kernel estimates for a vector of multiple independent onedimensional stable processes 
11:0011:20 
邓昌松 
Exact Asymptotic Formulas for the Heat Kernels of Space and TimeFractional Equations 
11:2011:40 
马丽 
一类随机泛函微分方程的Em逼近 
11:3015:00 
午餐休息 
Strong Uniqueness of Degenerate SDEs with Sobolev Diffusion coefficients
张希承
武汉大学
Abstract：We prove a new strong uniqueness result and a weak existence result for possibly degenerate multidimensional stochastic differential equations with Sobolev diffusion coefficients and rough drifts. Examples with Holder diffusion coefficients are also provided to show our results.
QuasiLinear SPDE with TimeFractional Derivatives
刘伟
江苏师范大学
Abstract: In this talk we present a method to solve (stochastic) evolution equations on Gelfand triples with timefractional derivative based on monotonicity techniques. Applications include deterministic and stochastic quasilinear partial differential equations with timefractional derivatives, including timefractional (stochastic) porous media equations (including the case where the Laplace operator is also fractional) and pLaplace equations as special cases. This talk is mainly based on the joint work with Michael Roeckner and Jose Luis da Silva.
Cauchy principal values of some integral functionals driven by a fractional Brownian motion
闫理坦
东华大学
Abstract：In this talk, we consider the Cauchy principal values of some integral functionals driven by a fractional Brownian motion with arbitrary Hurst index. Some calculus and limit theorems associated with these integral functionals are introduced.
Wellposed and large deviations for 2D Stochastic NavierStokes equations with jumps
翟建梁
中国科学技术大学
Abstract: Under the classical Lipschitz and linear growth assumptions, we established the existence and uniqueness of strong (in probability sense and PDE sense) solutions for 2D Stochastic NavierStokes equations driven by multiplicative Lévy noise. And we established WentzellFreidlin type large deviation principles for the solutions.
Random attractor for the 2D stochastic nematic liquid crystals flows with multiplicative noise
周国立
重庆大学
Abstract: Under nonperiodic boundary conditions, we consider the longtime behavior for stochastic 2D nematic liquid crystals flows with velocity and orientations perturbed by additive noise and multiplicative noise respectively.
The presence of the noises destroys the basic balance law of the nematic liquid crystals flows, so we can not follow the standard argument to obtain uniform a priori estimates for the stochastic flow under Dirichlet boundary condition and Numann boundary condition for velocity field and orientation field respectively. To overcome the difficulty our idea is to use some kind of logarithmic energy estimates and Ito formula in some Banach space to obtain the uniform estimates which improve the previous result for the orientation field that grows exponentially w.r.t.time t. In order to study the existence of random attractor, we need to show the solution is a stochastic flow. But this is not obvious because of the emergence of this kind of multiplicative noise in the orientation field. We give a short proof which is highly nontrivial to show the flow property of the orientation field. Our idea is to construct several linear stochastic partial differential equations whose scalar valued solutions are stochastic flow, then by discussing the relationship between these scalar equations and orientation field equation we prove that the each component of orientation field is indeed a stochastic flow . Since the global wellposedness is only established for the weak solution, to consider the existence of random attractor, the common method is to derive uniform a priori estimates in functional space which is more regular than the weak solution space. However, the common method fails because of the illposedness of the strong solution. Here, our idea is that by proving the compactness property of the stochastic flow and regularity of the solutions we construct a compact absorbing ball in the weak solution space which implies the existence of the random attractor. It is\ $\mathbf{the}$\ $\mathbf{first}$ $\mathbf{result}$ for the longtime behavior of stochastic nematic liquid crystals under Dirichlet boundary condition for velocity field and Neumann boundary condition for orientation field.
On Approximations of the EulerPeano scheme for Multivalued stochastic differential equations
巫静
中山大学
Abstract: In this work we apply the EulerPeano scheme to show that existence of weak solution and pathwise uniqueness still hold for multivalued stochastic differential equations when the coefficients are random and satisfy onesided locally Lipschitz continuous and an integral condition. When the coefficients are nonrandom and possibly discontinuous, the sequence of solutions of the EulerPeano scheme converges weakly, and the limit is a weak solution of the corresponding MSDE. We also obtain a global semiflow for stochastic differential equations reflected in closed, convex domains.
Stochastic porous media equation on general measure spaces with increasing Lipschitz nonlinearities
武伟娜
南京财经大学
Abstract: We prove the existence and uniqueness of probabilistically strong solutions to stochastic porous media equations driven by timedependent multiplicative noise on general measure spaces, and the Laplacian replaced by a negative definite selfadjoint operator L. In the case of Lipschitz nonlinearities $\Psi$, we in particular generalize previous results for open domain in $\mathbb{R}^d$ and L=Laplacian to fractional Laplacians. We also generalize known results on general measure spaces, where we succeeded in dropping the transience assumption on L, in extending the set of allowed initial data and in avoiding the restriction to superlinear behavior of $\Psi$ at infinity for $L^2$initial data.
Largetime behaviors of the heat equation under the generalized curvaturedimension inequality
黎怀谦
天津大学应用数学中心
Abstract: We mainly talk about the largetime behaviors of the heat kernel and the solution to the heat equation under the generalized curvaturedimension inequality introduced by Baudoin–Garofalo. For the later, the moment bound type of estimates for the nonnegative solution to the heat equation in the spirit of J. Nash are established. Also, the mean value property of bounded harmonic functions at infinity is studied. All the results parallel or partially generalize the main ones in the particular context of Riemannian manifold with nonnegative Ricci curvature.
Application of Poisson approach in occupation times
李应求
长沙理工大学
Abstract: We adopt the Poisson approach of Li and Zhou(2014) to consider the joint Laplace transform of occupation times for SNLP and diffusion processes. We discuss the occupation times related first exiting time and last exiting time, and obtain some results: 1)Occupation times over intervals (a,r)$and (r,b) before it first exits from either a or b. 2) Potential measures that are discounted by joint occupation times over semiinfinite intervals $(\infty, a)$ and $(a, +\infty)$. 3)Joint Laplace transforms involving the last exit time(from a semiinfinite interval), the value of the process at the last exit time and associate occupation time.
随机变量的收敛性和大数定律
胡泽春
四川大学
Abstract：本报告将基于以下2篇论文介绍我们在随机变量的收敛性和大数定律方面的几点工作：
1.Jiyanglin Li, ZeChun Hu: Toeplitz lemma, complete convergence and complete moment convergence, Communication in Statistics  Theory and Methods, 46(4), 17311743 (2017).
2.ZeChun Hu, Xue Peng, Wei Sun: Convergence of random variables and the law of large numbers, In preparation.
The first order correction to harmonic measure for random walks of rotationally invariant step distribution
向开南
南开大学
Abstract：In this talk, I will describe a progress on a universality conjecture on the first order correction to Brownian harmonic measure for random walks with bounded jumps. The talk is based on a joint work with Wang Longmin（王龙敏）and Zou Lang（邹浪）.
Properties of martingales under sublinear expectations
宋永生
中国科学院
Abstract：In this talk, I shall give an introduction to the structure and properties of martingales under sublinear expectations.
ContinuousTime Portfolio and Consumption Decisions under Loss Aversion
毕秀春
中国科学技术大学
Abstract: We investigate continuoustime optimal portfolio and consumption problems under loss aversion in an infinite horizon. The investor's goal is to choose optimal portfolio and consumption policies to maximize total discounted Sshaped utility from consumption. The optimal consumption and portfolio policies are obtained through the martingale method and replication technique. Numerical results indicate the differences between the loss averse investor and the constant relative risk averse (CRRA) investor on the optimal consumption and portfolio policies: the loss averse investor likes consuming more money but exposing less to risk than that of the CRRA investor, and the optimal wealth, as a function of state price density, drops faster for the CRRA investor than that for the loss averse investor.
Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles
刘党政
中国科学技术大学
Abstract: We compare finite rank perturbations of the following three ensembles of complex rectangular random matrices: First, a generalised Wishart ensemble with one random and two fixed correlation matrices introduced by Borodin and Peche, second, the product of two independent random matrices where one has correlated entries, and third, the case when the two random matrices become also coupled through a fixed matrix. The singular value statistics of all three ensembles is shown to be determinantal and we derive double contour integral representations for their respective kernels. Three different kernels are found in the limit of infinite matrix dimension at the origin of the spectrum. They depend on finite rank perturbations of the correlation and coupling matrices and are shown to be integrable. The first kernel (I) is found for two independent matrices from the second, and two weakly coupled matrices from the third ensemble. It generalises the Meijer Gkernel for two independent and uncorrelated matrices. The third kernel (III) is obtained for the generalised Wishart ensemble and for two strongly coupled matrices. It further generalises the perturbed Bessel kernel of Desrosiers and Forrester. Finally, kernel (II), found for the ensemble of two coupled matrices, provides an interpolation between the kernels (I) and (III), generalising previous findings of part of the authors.
This is based on joint work with G. Akemann, T. Checinski and E. Strahov
On stiff problems via Dirichlet forms
李利平
中国科学院
Abstract: The stiff problem is concerned with the thermal conduction model with a very small barrier, which is treated as a singular material of zero volume. In this talk, we shall build a phase transition for the stiff problem in onedimensional space and that related to the Walsh's Brownian motion. It turns out that the phase transition fairly depends on the total thermal resistance of the barrier, and the three phases corresponds to the socalled impermeable pattern, semipermeable pattern and permeable pattern of thermal conduction respectively. For each pattern, the related boundary condition at the barrier of the flux will be also derived. Mathematically, we shall introduce and explore the socalled snapping out Markov process, which is the probabilistic counterpart of semipermeable pattern for the stiff problem. We refer to arXiv: 1804.02634 for this recent work.
Longterm behaviors of stochastic flows of continuousstate branching processes and extremal processes
马春华
南开大学
Abstract: A class of stochastic flows of continuous state branching process were constructed by Legall and Bertoin (2000) and Dawson and Li (2012) through subordinators and SDEs respectively. In this work, we study the longterm behavior of flows of continuousstate branching processes through extremal processes, which arise in the case of supercritical processes with infinite mean and of subcritical processes with infinite variation. The jumps of these extremal processes are interpreted as specific initial individuals whose progenies overwhelm the population. These individuals, which correspond to the records of a certain Poisson point process embedded in the flow, are called superindividuals. They radically increase the growth rate to +∞ in the supercritical case, and slow down the rate of extinction in the subcritical one.
Uniqueness in law for stablelike processes of variable order
金鹏
University of Wuppertal
White noise solution to 2D stochastic Euler equations
罗德军
中国科学院
Abstract: We consider the weak vorticity formulation of the 2D Euler equations perturbed by transport type multiplicative noises. It is known that the white noise measure is the weak limit of point vortices when the number of vortex points goes to infinity. Based on this fact, we show that, under suitable conditions, the 2D stochastic Euler equation has a white noise solution, namely, the law of the solution is absolutely continuous with respect to the white noise measure at any time. Moreover, the density function satisfies a gradient estimate and the FokkerPlanck equation. This is a joint work with Franco Flandoli.
Heavy tail and light tail of CoxIngersollRoss processes with regimeswitching
邵井海
天津大学
Abstract: In this talk, we shall introduce some results on the tail behavior of the CoxIngersollRoss (CIR) processes with regimeswitching. One essential difference between CIR process with regimeswitching and without regimeswitching is: the stationary distribution for CIR process with regimeswitching could be heavytailed, however, without switching, the corresponding stationary distribution must be lighttailed. Our results provide a theoretical evidence of the existence of regimeswitching for interest rates model based on its heavytailed empirical evidence. In this work, we first provide sharp criteria to justify the existence of stationary distribution for the CIR process with regimeswitching, which is applied to study the long term returns of interest rates. Then under the existence of the stationary distribution, we provide a criterion to justify whether its stationary distribution is heavytailed or not.
Stabilization of regimeswitching processes by feedback control based on discrete time observations II: statedependent case
席福宝
北京理工大学
Abstract: This work investigates the almost sure stabilization of a class of regimeswitching systems based on discretetime observations of both continuous and discrete components. It develops Shao's work [SIAM J. Control Optim., 55(2017), pp. 724740] in two aspects: first, to provide sufficient conditions for almost sure stability in lieu of moment stability; second, to investigate a class of statedependent regimeswitching processes instead of stateindependent ones. To realize these developments, we establish an estimation of the exponential functional of Markov chains based on the spectral theory of linear operator. Moreover, through constructing suitable coupling processes based on Skorokhod's representation of jumping process, we realize the control from up and below of the evolution of statedependent switching process by stateindependent Markov chains. In addition, we also append an explicit construction of the general processes of regimeswitching systems based on discretetime observations. (Joint work with Jinghai Shao.)
Ergodicity for SDEs Driven byαStable processes with Markov switching
张振中
东华大学
Abstract: In this talk , we consider the ergodicity for stochastic differential equations driven by symmetric αstable processes with Markovian switching inWasserstein distances. Some sufficient conditions for the exponential ergodicity are presented by using the theory of Mmatrix, coupling method and Lyapunov function method. As applications, the OrnsteinUhlenbeck type process and some other processes driven by symmetric αstable processes with Markovian switching are presented to illustrate our results. In addition, under some conditions, an explicit expression of the invariant measure for OrnsteinUhlenbeck process is given.
Functional inequalities on loop space over a general noncompact manifold
陈昕
上海交通大学
Abstract: We will prove several asymptotic gradient estimates for heat kernel on a general noncompact manifold. Based on these estimates, we could construct an OU Dirichlet form on loop space over a general noncompact manifold which is only complete and stochastically complete. Moreover, a local logSobolev inequality and a logSobolev inequality with potential term will also be established. This talk is based on a joint work with XueMei Li and Bo Wu.
Dirichlet heat kernel estimates for a vector of multiple independent onedimensional stable processes
胡二彦
天津大学
Abstract：Consider, in ddimensional Euclidean space, a vector $X$ of d independent onedimensional symmetric stable processes of order $\alpha$. We are concerned with twosided Dirichlet heat kernel estimates of $X$ on $C^{1,1}$ domains in $\mathbb{R}^d$. Our results are sharp in some domains satisfying certain conditions. This is a joint work with Professor ZhenQing Chen and Guohuan Zhao.
Exact Asymptotic Formulas for the Heat Kernels of Space and TimeFractional Equations
邓昌松
武汉大学
Abstract: We study the asymptotic behaviour of the fundamental solutions (heat kernels) of nonlocal (partial and pseudo differential) equations with fractional operators in time and space. In particular, we obtain exact asymptotic formulas for the heat kernels of timechanged Brownian motions and Cauchy processes. This talk is based on a joint work with Prof. Rene Schilling (TU Dresden, Germany).
一类随机泛函微分方程的Em逼近
马丽
海南师范大学
Abstract:我们将介绍一类带Levy跳的中立随机微分方程的Euler近似解。利用Gronwall不等式、Holder不等式及BDG不等式，在局部Lipschitz条件和线性增长下，证明了近似解在均方意义下收敛于真实解。还将介绍一类带有限延迟的随机泛函微分方程的EM逼近，定义了该方程的带随机步长的EM算法，得到了随机步长的两个特点：有限个步长求和是停时；可列无限多个步长求和是发散的。最终由离散形式的非负半鞅收敛定理得到了在系数满足局部Lipschitz条件和单调条件下，带随机步长的EM数值解几乎处处收敛到零。
姓名 
职称 
单位 

毕秀春 
副研究员 
中国科技大学 

陈传钟 
教授 
海南师范大学 

陈昕 
特别研究员 
Chenxin217@sjtu.edu.cn 
上海交通大学 
陈晔 
讲师 
chenyexfw@163.com 
湖南文理学院 
陈勇 
副教授 
湖南科技大学 

邓昌松 
副教授 
dengcs@whu.edu.cn 
武汉大学 
董昭 
研究员 
zdong@amt.ac.cn 
中国科学院 
高武军 
讲师 
gaowj@sustc.edu.cn 
南方科技大学 
韩新方 
副教授 
xfanghan@163.com 
海南师范大学 
郝子墨 
研究生 
武汉大学 

胡二彦 
讲师 
eryan.hu@tju.edu.cn 
天津大学 
胡泽春 
教授 
zchu@scu.edu.cn 
四川大学 
金鹏 
讲师 
pjin1982@googlemail.com 
University of Wuppertal 
黎怀谦 
副教授 
huaiqianlee@gmail.com 
天津大学应用数学中心 
李金芸 
实验员 
海南师范大学 

李利平 
助理研究员 
liliping@amss.ac.cn 
中国科学院 
李霓 
副教授 
海南师范大学 

李彤 
研究生 
tongli0510@126.com 
中山大学 
李英 
讲师 
527651108@qq.com 
湘潭大学 
李应求 
教授 
liyq2001@163.com 
长沙理工大学 
廖波 
教授 
海南师范大学 

刘党政 
副教授 
中国科学技术大学 

刘伟 
教授 
江苏师范大学 

罗德军 
副研究员 
luodj@amss.ac.cn 
中国科学院 
吕广迎 
副教授 
gylvmaths@126.com 
河南大学 
马春华 
副教授 
mach@nankai.edu.cn 
南开大学 
马丽 
副教授 
malihnsd@163.com 
海南师范大学 
马志明 
院士 
中国科学院 

彭雪 
讲师 
pengxuemath@scu.edu.cn 
四川大学 
任永 
教授 
renyong@126.com 
安徽师范大学 
邵井海 
教授 
shaojh@bnu.edu.cn 
天津大学 
申广君 
教授 
gjshen@163.com 
安徽师范大学 
宋将 
研究生 
海南师范大学 

宋永生 
副研究员 
yssong@amss.ac.cn 
中国科学院数学数学与系统科学研究院 
王立飞 
讲师 
flywit1986@163.com 
河北师范大学 
王荔丹 
讲师 
lidanw@nankai.edu.cn 
南开大学 
王珍 
研究生 
武汉大学 

韦东 
研究生 
海南师范大学 

魏茸 
研究生 
海南师范大学 

温馨 
研究生 
244172482@qq.com 
中山大学 
巫静 
副教授 
wjjosie@hotmail.com 
中山大学 
吴明燕 
研究生 
武汉大学 

武伟娜 
讲师 
wuweinaforever@163.com 
南京财经大学 
席福宝 
教授 
xifb@bit.edu.cn 
北京理工大学 
夏鹏程 
研究生 
武汉大学 

向开南 
教授 
kainanxiang@nankai.edu.cn 
南开大学 
闫理坦 
教授 
东华大学 

杨明 
研究生 
海南师范大学 

杨赛赛 
博士 
中国科技大学 

翟建梁 
副教授 
Zhaijl@ustc.edu.cn 
中国科学技术大学 
张 登 
副教授 
dzhang@sjtu.edu.cn 
上海交通大学 
张希承 
教授 
XichengZhang@gmail.com 
武汉大学 
张裕华 
研究生 
海南师范大学 

张振中 
副教授 
zzzhang@dhu.edu.cn 
东华大学 
赵国焕 
博士后 
zhaoguohuan@gmail.com 
中国科学院 
周国立 
副教授 
zhouguoli736@126.com 
重庆大学 
祖力 
副教授 
zulihsd2014@163.com 
海南师范大学 
海南省数学研究中心是海南省教育厅2016年8月批准成立的省级研究平台。中心挂靠海南师范大学数学与统计学院，归口海南师范大学管理，其职责为：整合全省资源，做好海南省数学学科建设，努力创建一流数学学科；开展多种形式的学术交流、协同创新、科研攻关、实践教学、数学教师培训、中小学夏令营（冬令营）等活动。
首届中心主任由国际著名数学家，德国马克斯普朗克莱比锡数学所所长、德国自然科学院院士Jurgen Jost教授担任；海南师范大学数学与统计学院院长陈传钟教授任执行主任。中心设有海南省院士工作站，中国科学院马志明院士、严加安院士及其团队已入站开展工作。现有概率论及其应用，组合图论及其优化，函数论与几何分析，动力系统与生物数学，量子信息与数学物理，大数据、云计算与网络安全6个研究方向。有专兼职科研人员29人，其中柔性引进海外高层次人才5人。此外，中心还聘有中学一线优秀骨干教师26人，协同中心科研人员共同开展海南数学基础教育的改革与实践研究。
中心成立1年多以来，已经形成了较为稳定和具有较强科研创新能力的研究团队，组织开展了丰富多彩的学术交流活动。中心正按照“十三五”发展规划积极开展各项建设，努力为海南打造一流数学学科做出贡献。
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