From Uniform Limit Theorems for Markov Chains to Maximal Points in Planar Regions

Abstract

In this talk I will present the results I obtained in the last few years. The first topic "uniform limit theorems for Markov chains" is the subject matter of my PhD Thesis. Uniform limit theorems for iid observations have been extensively studied in the Probability and Statistics literature; in contrast the corresponding theorems for Markov chains received little attention due to complexity of dependence. I will give results on uniform CLT and LIL for Markov chains. The second topic on distributional properties of maximal points in planar regions is based on joint work with Bai, Hwang and Liang. CLT and Poisson approximation results will be presented.