关于可列非齐次马氏链的若干极限定理

Some limit theorems for non-homogeneous Markov chains

设{Xn,n≥0}是一列非齐次马尔科夫链,{an,n≥0}是一列固定的非负整数序列.首先构造了一个带参数的广义似然比函数,然后利用Borel-Cantelli引理证明随机变量序列几乎处处收敛性,得到了关于可列非齐次马氏链序偶广义平均的若干极限定理,推广了已有的结果.

Let {Xn,n≥0}be a sequence of nonhomogeneous Markov chains and {an,n≥0} be a fixed sequence of non-negative integers. In this paper, we first construct a generalized likelihood ratio function with a parameter, then by using the Borel-Cantelli Lemma to prove the almost everywhere convergence of random variables, we obtain some limit theorems for countable nonhomogeneous Markov chains of ordered couple of generalized mean, which generalize some existing results.