浙江大学概率统计研讨会

浙江大学概率统计研讨会时间：2017年11月18-19日地点：杭州申花路796号紫金港国际饭店（近浙大紫金港校区）18日上午: 9:30-10:10 肖益民Michigan State University 10:10-10:50 李哲骅上海纽约大学10:50-11:05 茶歇11:05-11:45 陈新兴上海交通大学18日下午: 13:30-14:10 周望新加坡国立大学14:10-14:50 李利平中科院14:50-15:05 茶歇15:05-15:45 Sergey Bocharov 浙江大学15:45-16:25 王文胜杭州电子科技大学16:25-16:35 茶歇16:35-17:15 潘光明新加坡南洋理工大学19日上午: 9:00-9:40 张立新浙江大学9:40-10:20 张登上海交通大学10:20-10:40 茶歇10:40-11:20 李育强华东师范大学11:20-12:00 陈娴厦门大学联系人：苏中根 suzhonggen@赵敏智 zhaomz@欢迎大家参加！浙江大学概率统计研讨会地点：杭州申花路796号紫金港国际饭店（近浙大紫金港校区）New directions in studies of sample functions of Levy and Levy-Typeprocesses肖益民Michigan State UniversityDiscretize Brownian bridge on manifolds李哲骅上海纽约大学Gaussian bounds on locally irregular graphs陈新兴上海交通大学A well known theorem of Delmotte is that Gaussian bounds, parabolic Harnack inequality, and the combination of volume doubling and Poincare inequality are equivalent for graphs. In this paper we consider graphs for which these conditions hold, but only for sufficiently large balls, and prove a similar equivalence.Canonical correlation coefficients of high-dimensional Gaussianvectors: finite rank case周望新加坡国立大学On the Dirichlet form of three-dimensional Brownian motionconditioned to hit the origin李利平中科院Branching Brownian Motion with spatially-homogeneous andpoint-catalytic branchingSergey Bocharov 浙江大学We shall discuss the asymptotics of the rightmost particle in the model of branching Brownian motion in which the usual spatially-homogeneous branching and catalytic branching at a single point are simultaneously present.Functional-coefficient spatial regression王文胜杭州电子科技大学Limiting laws for divergent spiked eigenvalues and largest non-spiked eigenvalue of sample covariance matrices潘光明新加坡南洋理工大学We study the asymptotic distributions of the spiked eigenvalues and the largest nonspiked eigenvalue of the sample covariance matrix under a general covariance matrix model with divergent spiked eigenvalues, while the other eigenvalues are bounded but otherwise arbitrary. The limiting normal distribution for the spiked sample eigenvalues is established. It has distinct features that the asymptotic mean relies on not only the population spikes but also the nonspikes and that the asymptotic variance in general depends on the population eigenvectors. In addition, the limiting Tracy-Widom law for the largest nonspiked sample eigenvalue is obtained. Estimation of the number of spikes and the convergence of the leading eigenvectors are also considered. The results hold even when the number of the spikes diverges.Recursive stochastic algorithms with applications to adaptive designs张立新浙江大学Stochastic approximation algorithms have been the subject of an enormous body of literature, both theoretical and applied. By using a central limit theorem for the stochastic approximation algorithm, Laruelle and Pages (Ann. Appl. Probab., 2013) derived the asymptotic normality or central limit theorem for randomized urn models investigated in Bai and Hu (Ann. Appl. Probab., 2005). However, the classical central limit theorem for the stochastic approximation algorithm does not include all cases of its regression function, creating a gap between the results of Laruelle and Pages (2013) and those of Bai and Hu (2005) for randomized urn models. We establish new central limit theorems of the stochastic approximation algorithm under the popular Lindeberg condition to fill this gap. In our applications, we investigate a more involved family of urn models and related adaptive designs in which it is possible to remove the balls from the urn, and the expectation of the total number of balls updated at each stage is not necessary a constant. The asymptotic properties are derived under much less stringent assumptions than those in Bai and Hu (2005) and Laruelle and Pages (2013). In this talk, I will mainly talk about the relationship and application of the stochastic approximation algorithms to various randomization models in clinical trials.Optimal bilinear control of stochastic nonlinear Schrödinger equations driven by linear multiplicative noise张登上海交通大学In this talk we consider the optimal bilinear control problem of quantum mechanical systems with final observation governed by a stochastic nonlinearSchrödinger equation with linear multiplicative noise. The existence of an open loop optimal control and first order Lagrange optimality conditions are derived, via Skorohod's representation theorem, Ekeland's variational principle and the existence for the linearized dual backward stochastic equation. The approach in particular applies to the deterministic case. This is a joint work with Viorel Barbu and Michael Röckner.Fractional martingales arising from branching stable processes李育强华东师范大学Mathematical foundation of nonequilibrium fluctuation-dissipation theorems for inhomogeneous diffusion processes with unboundedcoefficients陈娴厦门大学Nonequilibrium fluctuation-dissipation theorems (FDTs) are one of the most important advances in stochastic thermodynamics over the past decade. Here we provide a rigourous mathematical theory of two types of nonequilibrium FDTs for inhomogeneous diffusion processes with unbounded drift and diffusion coefficients by using the Schauder estimates for partial differential equations of parabolic type and the theory of weakly continuous semigroups. The FDTs proved in this paper apply to any forms of nonlinear external perturbations. Moreover, we clarify the precise mathematical conditions and ranges of applicability for the two types of FDTs. Examples are also given to illustrate the main results of this paper. This is a joint work with Chen Jia.。