Hoeffding's inequality for Markov processes via solution of Poisson's equation

作     者：Yuanyuan LIU Jinpeng LIU Yuanyuan LIU;Jinpeng LIU

作者机构：School of Mathematics and StatisticsNew CampusCentral South UniversityChangsha 410083China 

出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)

年 卷 期：2021年第16卷第2期

页      面：543-558页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：This work was supported in part by the National Natural Science Foundation of China(Grant Nos.11971486,11771452) the Natural Science Foundation of Hunan Province(Grant Nos.2019JJ40357,2020JJ4674) the Innovation Program of Central South University(Grant No.2020zzts039) 

主　　题：Hoeffding's inequality Markov process Poisson's equation 

摘      要：We investigate Hoeffding s inequality for both discrete-time Markov chains and continuous-time Markov processes on a general state space. Our results relax the usual aperiodicity restriction in the literature, and the explicit upper bounds in the inequalities are obtained via the solution of Poisson s equation. The results are further illustrated with applications to queueing theory and reective diffusion processes.