A PROBABILITY APPROXIMATION FRAMEWORK: MARKOV PROCESS APPROACH

被引：1

作者：

Chen, Peng ^{[1
]}

Shao, Qi-Man ^{[2
]}

Xu, Lihu ^{[3
]}

机构：

[1] Nanjing Univ Aeronaut & Astronaut, Coll Math, Nanjing, Peoples R China

[2] Southern Univ Sci & Technol, Dept Stat & Data Sci, SICM, NCAMS, Shenzhen, Peoples R China

[3] Univ Macau, Fac Sci & Technol, Dept Math, Zhuhai, Peoples R China

来源：

ANNALS OF APPLIED PROBABILITY | 2023年 / 33卷 / 02期

关键词：

Probability approximation; Markov process; It??s formula; online stochastic gradient descent; stochastic differential equation; Euler-Maruyama (EM) discretization; stable process; normal approxi-mation; Wasserstein-1; distance; MULTIVARIATE NORMAL APPROXIMATION; STEINS METHOD; POISSON APPROXIMATION; INVARIANT-MEASURES; MATRICES; ERGODICITY; EQUATIONS; DISTANCE; MODEL;

D O I：

10.1214/22-AAP1853

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：1419 / 1459

页数：41

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