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

DOI: 10.12677/PM.2016.61012, PP. 81-87

Keywords: 马氏链，马氏环境，强极限定理，相对熵
Markov Chain, Markov Environments, Strong Limit Theorem, Relative Entropy

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Abstract:

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。
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.

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