报告时间：2025年05月12日（星期一）10:00-11:00

报告地点：翡翠湖校区科教楼B座1710室

报 告 人：肖益民 教授

工作单位：Michigan State University

举办单位：数学学院

报告简介：

Local times of a random field X ={X(t), t\in \mathbb{R}^N} with values in \mathbb{R}^N carry a lot of analytic and geometric properties about X. They also arise naturally in the limit distributions of functionals of integrated and fractionally integrated time series or spatial processes, and in nonlinear cointegrating regression. After an overview of local times and their applications, we will focus on the local times of anisotropic Gaussian random fields satisfying strong local nondeterminism with respect to an anisotropic metric. By applying moment estimates for local times, we prove optimal local and global Holder conditions for the local times for these Gaussian random fields and deduce related sample path properties. These results are closely related to Chung's law of the iterated logarithm and the modulus of nondifferentiability of the Gaussian random fields.We apply the results to systems of stochastic heat equations with additive Gaussian noise and determine the exact Hausdorff measure function for the level sets of the solution.The second part of the talk is based on a joint paper with Cheuk Yin Lee.

报告人简介：

肖益民教授，Department Statistics and Probability, Michigan State University, Foundation Professor. 2011年当选为美国数理统计学会会士。主要从事随机场及随机偏微分方程，分形几何，位势理论，随机场的极值理论，空间统计，非参数估计方面的研究，并取得了一系列具有国际先进水平的重要成果，在国际知名数学和统计杂志发表学术论文150余篇，在数十种主要国际会议上做大会专题发言；自1998年至今，主持或共同主持美国国家自然科学基金项目十三项。曾担任SCI杂志《Statistics and Probability Letters》（统计和概率通讯）共同主编（2011-2022），现担任《Science in China, Mathematics》（中国科学，数学），《Illinois Journal of Mathematics》（伊利诺伊数学杂志）《Journal of Fractal Geometry》（分形几何杂志）的编委。多次担任美国国家自然科学基金概率和统计项目评审小组成员，以及加拿大，瑞士，德国，香港等国家和地区自然科学基金评审人。在Annals of Probability，Probability Theory and Related Fields, Journal of Theoretical Probability, Electronic Journal of Probability, Bernoulli, Annals of Applied Probability, Journal of Differential Equations, Journal Of Mathematical Analysis And Applications, Statistics and Probability Letters等国际一流期刊发表论文。

主要的研究领域：Stochastic Processes and Random Fields (Gaussian random fields; matrix-valued random fields; infinitely divisible random fields; Levy processes; and Markov processes); Stochastic Partial Differential Equations；Statistical Analysis of Random Field Models (Estimation and prediction); Extreme Value Theory; Random Fractals, Geometry of Fractals。