A PROBABILITY APPROXIMATION FRAMEWORK: MARKOV PROCESS APPROACH

• 成果类型: Article
• 署名作者: Chen, Peng; Shao, Qi-Man; Xu, Lihu
• 署名单位: Nanjing University of Aeronautics & Astronautics; Southern University of Science & Technology; University of Macau
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1853
• 发表日期: 2023
• 页码: 1419-1459
• 关键词: multivariate normal approximation; steins method; Poisson approximation; invariant-measures; matrices; ergodicity; EQUATIONS; distance; MODEL

摘要

We view the classical Lindeberg principle in a Markov process setting to establish a probability approximation framework by the associated Ito's for-mula and Markov operator. As applications, we study the error bounds of the following three approximations: approximating a family of online stochastic gradient descents (SGDs) by a stochastic differential equation (SDE) driven by multiplicative Brownian motion, Euler-Maruyama (EM) discretization for multi-dimensional Ornstein-Uhlenbeck stable process and multivariate nor-mal approximation. All these error bounds are in Wasserstein-1 distance.