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

共 50 条

[21] LEVY APPROXIMATION OF AN IMPULSE RECURRENT PROCESS WITH MARKOV SWITCHING
Korolyuk, V. S.
Limnios, N.
Samoilenko, I. V.
THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS, 2009, 80 : 15 - 22
[22] On Poisson approximation to the partial sum process of a Markov chain
He, SW
Xia, AH
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1997, 68 (01) : 101 - 111
[23] Caged Markov process - A continuous-time framework for modeling a constrained Markov process within a freely-evolving Markov process
Printechapat, Tanes
Aiewsakun, Pakorn
Krityakierne, Tipaluck
MATHEMATICS AND COMPUTERS IN SIMULATION, 2025, 230 : 350 - 369
[24] APPROXIMATION OF INVARIANT PROBABILITY MEASURE OF A MARKOV KERNEL WITH RESPECT TO WEAK-CONVERGENCE
WOLF, D
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 1980, 60 (7BIS): : T372 - T374
[25] Dynamic Bayesian Ratemaking: A Markov Chain Approximation Approach
Li, Hong
Lu, Yang
Zhu, Wenjun
NORTH AMERICAN ACTUARIAL JOURNAL, 2021, 25 (02) : 186 - 205
[26] Optimal portfolio execution with a Markov chain approximation approach
Chen, Jingnan
Feng, Liming
Peng, Jiming
Zhang, Yu
IMA JOURNAL OF MANAGEMENT MATHEMATICS, 2023, 34 (01) : 165 - 186
[27] ESTIMATION OF EXTINCTION PROBABILITY OF A MULTITYPE MARKOV BRANCHING-PROCESS
KALE, MM
DESHMUKH, SR
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 1993, 22 (04) : 1195 - 1206
[28] Probability functional of a vector non-Gaussian Markov process
Lyandres, V
PROCEEDINGS OF THE IEEE SIGNAL PROCESSING WORKSHOP ON HIGHER-ORDER STATISTICS, 1999, : 247 - 250
[29] OPTIMAL STOPPING OF MARKOV RENEWAL PROCESS WITH LOW ABSORPTION PROBABILITY
ANDREEV, NV
CYBERNETICS AND SYSTEMS ANALYSIS, 1994, 30 (06) : 938 - 942
[30] Markov Decision Process: Fuzzy approach
Kim, Chang Eun
Computers and Industrial Engineering, 1994, 27 (1-4): : 161 - 165

← 1 2 3 4 5 →