Convergence rate of Euler-Maruyama scheme to its invariant probability measure under total variation distance
数学学科创建110周年系列报告
报告题目(Title)：Convergence rate of Euler-Maruyama scheme to its invariant probability measure under total variation distance
报告人(Speaker)：叶印娜（西交利物浦大学）
地点(Place)：腾讯会议号431 232 848 密码 948950
时间(Time)：2025年5月16日（周五）10:00-11:00
邀请人(Inviter)：高志强
报告摘要
In this talk, we discuss the geometric decay rate of Euler-Maruyama scheme for one-dimensional stochastic differential equation towards its invariant probability measure under total variation distance. Firstly, the existence and uniqueness of invariant probability measure and the uniform geometric ergodicity of the chain are studied through introduction of non-atomic Markov chains. Secondly, the equivalent conditions for uniform geometric ergodicity of the chain are discovered, by constructing a split Markov chain based on the original Euler-Maruyama scheme. It turns out that this convergence rate is independent with the step size under total variation distance.
主讲人简介
Dr. Yinna Ye, Assistant Professor, Department of Applied Mathematics, School of Mathematics and Physics, Xi’an Jiaotong-Liverpool University (XJTLU). She received her Ph.D in Mathematics from University of Tours, France, in 2011. Before she joined XJTLU 2013, she was appointed as research and teaching assistant (ATER in French) in UoT and UBS. Her research interests lie in the area of probability limit theorems for the following models: Markov chains, branching processes in random environment, and branching random walks in random environment.
