随机环境中马氏链函数的极限性质  

THE LIMIT PROPERTIES FOR FUNCTION OF MARKOV CHAINS IN RANDOM ENVIRONMENTS

作　　者：黄敏 万成高 HUANG Min;WAN Cheng-gao(Faculty of Information and Engineering,Wuhan College,Wuhan 430212,China;College of Statistics and Mathematics,Zhongnan University of Economics and Law,Wuhan 430073,China;Faculty of Mathematics and Statistics,Hubei University,Wuhan 430062,China)

机构地区：[1]武汉学院信息工程学院,湖北武汉430212 [2]中南财经政法大学统计与数学学院,湖北武汉430073 [3]湖北大学数学与统计学学院,湖北武汉430062

出　　处：《数学杂志》2020年第5期585-592,共8页Journal of Mathematics

基　　金：国家自然科学基金资助(71974204)。

摘　　要：本文研究了随机环境中马氏链函数的极限性质的问题.利用构造鞅差序列的方法,获得了随机环境中马氏链函数强大数定律的一系列充分条件,即当函数列{gn(x),n≥0}中x的取值范围不同时,可取适合的函数得到相应的结论,从而推广了已有结论的适用范围.In this paper,we study the limit properties of Markov chain functions in random environments.By using the method of constructing martingale difference sequence,a series of sufficient conditions of the strong law of large numbers for Markov chain functions in random environment are obtained.That is,when the value range of x in the function sequence{gn(x),n≥0}is different,the appropriate function can be taken to obtain the corresponding conclusion,thus extending the scope of application of the existing conclusions.

关 键 词：随机环境 马氏链 强大数定律 

分 类 号：O211.62[理学—概率论与数理统计]