时 间：2023年11月21日 10:00-11:30
地 点: 腾讯会议ID：560-4756-7741
报告人：肖益民 密歇根州立大学教授
主持人：徐方军 华东师范大学教授
摘 要：
Local times of a Gaussian random field X = {X(t), t ∈ R^N } with values in R^d 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. In this talk, we study 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.
This talk is based on a joint paper with Cheuk Yin Lee.
报告人简介：
肖益民，美国密西根州立大学Foundation Professor。1996年博士毕业于美国俄亥俄州立大学, 2011年当选Fellow of Institute of Mathematical Statistics，曾担任期刊Statistics and Probability Letters的共同主编(2011-2022）。主要从事随机场、随机偏微分方程、分形几何、位势理论、随机场极值理论、空间统计和非参数估计等方面的研究。在Annals of Probability、Probability Theory and Related Fields、Annals of Applied Probability、Transactions of the AMS、Journal of London Mathematical Society等期刊发表论文160多篇。