A probability approximation framework: Markov process approach

2020/11/22 by Chen, Peng, Shao, Qi-Man, Xu, Lihu
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2011.10985

Abstract

We view the classical Lindeberg principle in a Markov process setting to establish a probability approximation framework by the associated Itô's formula 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 normal approximation. All these error bounds are in Wasserstein-1 distance.

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