随机环境中马氏链的常返与强常返

Recurrence and Strong Recurrence for Markov Chains in Random Environments

引出了随机环境中马氏链的π-不可约和强π-不可约性的定义,在强π-不可约条件下,得到了随机环境中马氏链强常返的充要条件以及随机环境中马氏链常返的判定准则,最后在π-不可约条件下讨论了常返与强常返的关系.

In this paper,we introduce the definition about the π-irrdeucibility and strong π-irrdeucibility for Markov chains in random environments.Some criterion that strong π-irrdeucibility Markov chains in random environment are recurrent are given,thereby the sufficient and necessary condition of strong recurrence of strong π-irrdeucibility Markov chains in random environments is obtained.The relation between recurrence and strong recurrence in the condition of strong π-irrdeucibility Markov chains in random environments is discussed.