平稳环境中马氏链的不可约性

The Irreducibility of Markov Chains in Random Environments

给出若单链X→具π-不可约性,则环境空间中的平稳分布π是遍历的,同时也指出在单链X→的状态空间有限的前提下,该单链是强常返的,从而推广了经典马氏链相应的结论.

In this paper, we prove that if single Markov chain X^→ is irreducible, then the stationary distribution in random environment be ergodic. We also point out that if the state space of single Markov chain is finite, the single Markov chain is strong recurrence which extend the corresponding theory in classical Markov chain.