有限状态下随机环境马氏链的性质

假设X是随机环境的马氏链,首先介绍了Hopf马氏链及绕积马氏链,利用绕积马氏链,定义了随机环境马氏链的几个特征数及随机环境马氏链的几种不同的基本状态,由此比较随机环境的马氏链与经典的时齐马氏链状态性质的异同,得到了随机环境马氏链中强常返与弱常返的关系,并进一步讨论了X为有限集时,随机环境的马氏链的一些性质,得到有限状态一定存在本质与弱常返状态,不一定存在强常返状态,及在可达关系下本质状态、强常返状态的关系.

Properties of Finite State Markov Chain in Random Environments

Let{X→} be Markov chains in random environments with finite or countable state space.Firstly,we introduce Hopf Markov chains and skew product Markov chains,and define some character number and some basic states on Markov chains in random environments.Then,we discuss the difference state properties between Markov chains in random environments and homogeneous Markov chains,and obtain the relationship of strongly recurrent state and weak recurrent state.Finally,when {X→} be finite,we prove existence of essential states and weak recurrent states;and if x is essential state or strongly recurrent state and x can lead to y,then y also is essential state or strongly recurrent state.