活动时间：2023-09-30 09:00
活动地点：腾讯会议 118-921-511
主讲人：肖益民
主讲人中文简介：
肖益民，密西根州立大学FoundationProfessor。主要从事随机场及随机偏微分方程，分形几何，位势理论，随机场的极值理论方面的研究。肖益民教授2011年当选为美国数理统计学会会士。是《Statistics and ProbabilityLetters》共同主编。同时还是《Science in China，Mathematics》《lllinois Journal of Mathematics》《Journal of Fractal Geometry》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。
活动内容摘要：
Local times of a Gaussian random fi eld 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 elds 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 elds and deduce related sample path properties. These results are closely related to Chung's law of the iterated logarithm and the modulus of nondi erentiability of the Gaussian random elds.
We apply the results to systems of stochastic heat equations with additive Gaussian noise and determine the exact Hausdor measure function for the level sets of the solution.
This talk is based on a joint paper with Davar Khoshnevisan and CheukYin Lee.
主持人：张振中