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
收藏
页码：1419 / 1459
页数：41
相关论文
共 50 条
12345