题目：Stable Random Fields: Regularity, LocalTimes, and Statistical Analysis

汇报人： 肖益民

会议时间：2025年5月16日（周五）15:30-16:30

地点：综合楼644会议室

报告人简介：

肖益民，密西根州立大学Foundation Professor。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 Probability Letters》共同主编。同时还是《Science in China, Mathematics》,《Illinois 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、德国和中国香港等国家和地区自然科学基金评审人。

报告摘要：

This talk is concerned with probabilistic and statistical analysis of stable random felds. Important examples of stable random fields include linear fractional stable motion, harmonizable fractional stable motion, and many more. 

We will focus on three aspects of the studies on stable random felds: regularity and fractal properties, localtimes, and statistical modeling and inference. In particular, we present some recent results on the uniform modulus of continuity, fractal dimension, and the local times of stable random fields. An important technical ingredient is the property of strong local nondeterminism, which is closely related to the prediction of stable random fields.