随机环境马氏链的状态分类

Classificatian of States On Markov Chain in Random Environment

假设■是随机环境的马氏链,本文首先介绍了Hopf马氏链及绕积马氏链,并介绍了随机环境马氏链中的几个特征数,由此定义了随机环境马氏链强常返,弱常返等壮态,在随机环境的马氏链下,讨论它们的关系,并进一步讨论了随机环境马氏链φ—不可约性及ψ—不可约性的性质,并在ψ—不可约下讨论了状态的性质,并获得在一定的条件下,必存在弱常返状态的结果。

Let（x^→） be Markov Chains in random environments with countable State space. In this paper, first of all ,we define Hopf Markov Chains and skew product Markov chain, and some character numbers of skew product Markov chain. By these character numbers , we introduce some basic concepts on the states ,such as strongly recurrent state ,weak recurrent state . and obtain their main properties. Further, we introduce φ--Irreducibility and φ-Irreducibility On Markov Chains in random environments. We investigate the properties of states ,and obtain the result of existence of weak recurrent state under some conditions.