单无限马氏环境下可列齐次马氏链的一类强偏差定理  

A CLASS OF SMALL DEVIATION THEOREM FOR HOMOGENEOUS MARKOV CHAINS IN MARKOVIAN ENVIRONMENT WITH COUNTABLE STATE SPACE

作　　者：石志岩[1] 周红[1] 丁承军 SHI Zhi-yan;ZHOU Hong;DING Cheng-jun(Faculty of Science,Jiangsu University,Zhenjiang 212013,China)

机构地区：[1]江苏大学数学科学学院,江苏镇江212013

出　　处：《数学杂志》2020年第5期611-623,共13页Journal of Mathematics

基　　金：国家自然科学基金(11971197;11601191;11571142);江苏大学青年英才计划;江苏省科协青年科技人才托举工程

摘　　要：本文研究了单无限马氏环境下可列齐次马氏链的一类强偏差定理.首先给出了单无限马氏环境下马氏链的定义和渐近对数似然比的概念,利用构造非负鞅的方法,获得了单无限马氏环境下可列齐次马氏链的强偏差定理,以及单无限马氏环境下可列齐次马氏链的强大数定律和Shannon-McMillan定理.In this paper,we study a small deviation theorem of Markov chains in singleinfinite Markovian environment on countable state space.Firstly,the definitions of Markov chain in single-infinite Markovian environment and the concept of the sample divergence distance are given.Then,by constructing non-negative martingale,we establish a class of small deviation theorems in single-infinite Markovian environment on countable state space.Meanwhile,the strong law of large numbers and Shannon-McMillan theorem in single-infinite random environment on countable state space are obtained.

关 键 词：马氏环境 马氏链 SHANNON-MCMILLAN定理 强偏差定理 

分 类 号：O211.6[理学—概率论与数理统计]