報告時間：2025年05月12日（星期一）10:00-11:00
報告地點：翡翠湖校區科教樓B座1710室
報 告 人：肖益民 教授
工作單位：Michigan State University
舉辦單位：數學學院
報告簡介：
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.
報告人簡介：
肖益民教授，Department Statistics and Probability, Michigan State University, Foundation Professor. 2011年當選為美國數理統計學會會士。主要從事隨機場及隨機偏微分方程，分形幾何，位勢理論，隨機場的極值理論，空間統計，非參數估計方面的研究，并取得了一系列具有國際先進水平的重要成果，在國際知名數學和統計雜志發表學術論文150余篇，在數十種主要國際會議上做大會專題發言；自1998年至今，主持或共同主持美國國家自然科學基金項目十三項。曾擔任SCI雜志《Statistics and Probability Letters》（統計和概率通訊）共同主編（2011-2022），現擔任《Science in China, Mathematics》（中國科學，數學），《Illinois Journal of Mathematics》（伊利諾伊數學雜志）《Journal of Fractal Geometry》（分形幾何雜志）的編委。多次擔任美國國家自然科學基金概率和統計項目評審小組成員，以及加拿大，瑞士，德國，香港等國家和地區自然科學基金評審人。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等國際一流期刊發表論文。
主要的研究領域：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。
