时 间：2021年11月17日（周三）10:00-11:00
地 点：线上，腾讯会议：680 707 248
题 目： Functional central limit theorems for stick-breaking priors
主讲人：Yaozhong Hu 加拿大阿尔伯塔大学数学和统计科学系教授
主持人：徐方军 教授
摘 要：
I will talk about the strong law of large numbers, Glivenko-Cantelli theorem, central limit theorem, functional central limit theorem for various nonparametric Bayesian priors which include the stick-breaking process with general stick-breaking weights, the two-parameter Poisson-Dirichlet process, the normalized inverse Gaussian process, the normalized generalized gamma process, and the generalized Dirichlet process. For the stick-breaking process with general stick-breaking weights, we will explain two general conditions such that the central limit theorem and functional central limit theorem hold. Except in the case of the generalized Dirichlet process, since the finite dimensional distributions of these processes are either hard to obtain or are complicated to use even they are available, we use the method of moments to obtain the convergence results. For the generalized Dirichlet process we use its marginal distributions to obtain the asymptotics although the computations are highly technical. This is joint work with Junxi Zhang.
报告人简介：
Yaozhong Hu(胡耀忠), 加拿大阿尔伯塔大学Centennial教授，1981年获江西大学计算数学学士学位，1984年获中科院武汉数学物理研究所硕士学位，1992年获法国路易斯巴斯德大学概率博士学位，师从国际著名概率学家P. A. Meyer教授。胡教授的研究兴趣广泛，主要研究领域是随机分析、数理金融、随机控制、随机微分方程数值分析等。在 Ann. Probability、Probab. Theory Related Fields、Ann. Applied Probability、Bernoulli、Stochatis Process. Appl.、Mem. Amer. Math. Soc.、Comm. PDEs、J. Funct. Anal、Trans. Amer. Math. Soc等概率论和数学综合类top期刊上发表论文100多篇，出版专著2部。2015年，当选为Fellow of Institute of Mathematical Statistics。