关于马氏环境中马氏链的一个极限性质
A Limit Property for Non-Homogeneous Markov Chain in Markov Environments

作者: 程 成 :安徽工业大学数理科学与工程学院,安徽 马鞍山;

关键词: 马氏链马氏环境强极限定理相对熵Markov Chain Markov Environments Strong Limit Theorem Relative Entropy

摘要:
本文研究马氏环境中非齐次马氏链泛函的滑动平均强极限性质。通过构造一列带参数且期望为1的随机变量,利用Borel-Cantelli引理来研究随机环境中马氏链的强极限定理,得到了马氏环境中马氏链泛函滑动平均的一个强极限定理,推广了若干已有结论。

Abstract: In this paper we discuss the strong limit properties for moving average of functions of non-ho- mogeneous Markov chain in Markov environments. By constructing a sequence of random va-riables with one parameter and take 1 as the expectation, with the aid of the classic Borel-Cantelli lemma, we study the strong limit properties of Markov chain in random environments and obtain a strong limit theorem for moving average of functions of non-homogeneous Markov chain in Markov environments. Moreover, we generalize the existing results.

文章引用: 程 成 (2016) 关于马氏环境中马氏链的一个极限性质。 理论数学, 6, 81-87. doi: 10.12677/PM.2016.61012

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