A probability approximation framework: Markov process approach

Peng Chen; Qi-Man Shao; Lihu Xu

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arXiv · 2011.10985

A probability approximation framework: Markov process approach

Peng Chen·Qi-Man Shao·Lihu Xu

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Abstract

We view the classical Lindeberg principle in a Markov process setting to establish a probability approximation framework by the associated It\^{o}'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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Peng Chen, Qi-Man Shao, Lihu Xu. 2020-11-22. A probability approximation framework: Markov process approach. https://arxiv.org/abs/2011.10985

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