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题目：Analysis of Multivariate Gaussian Random Fields

报告人： 肖益民

报告时间：2023年12月18日 8:30-9:30

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，香港等国家和地区自然科学基金评审人。

报告摘要：

In recent years, a number of classes of new multivariate random fields have been constructed by using the approaches of covariance matrices, variogram matrices, the convolution method, spectral representations, or systems of stochastic partial differential equations (SPDEs), and have been applied for modeling multivariate spatial or spatio-temporal data. However, the

theory of multivariate random fields in both probability and statistics is still under-developed. Consider a multivariate random field X = {X(t), t ∈ R N } taking values in R d defined by 

X(t) = (X1(t), · · · , Xd(t)), t ∈ R N .

Due to complicated dependence structures among the coordinate processes and anisotropies, 

In this talk, we present some recent results on the sample path and statistical properties of multivariate Gaussian random fields including multivariate Mat´ern Gaussian fields, operator fractional Brownian motion, and vector-valued operator-scaling random fields. These results illustrate explicitly the effects of the dependence structures among the component processes and anisotropies on the analytic and geometric properties of multivariate Gaussian random fields. An key technical ingredient for our studies is various notions of strong local nondeterminism for multivariate Gaussian random fields.