对双无限随机环境中的马氏链,给出了常返的两种可能的定义,讨论了它们间的联系和基本性质,给出了状态或链为常返的判断准则.讨论了双无限随机环境中马氏链的不变测度的存在性,首次给出了双无限随机环境中马氏链的正常返及零常返的概念,并讨论了其相关性质.特别地,应用不变函数的性质,给出了状态具有正常返性或零常返性的判断准则.

The two possible concepts of recurrence are introduced into the research field of Markov chains in bi-infinite random environments,and their connections and basic properties are discussed.Some criteria for states or chains to be recurrent are given.The existence of invariant measure of recurrent Markov chains in bi-infinite random environments are discussed.The concepts of positivity and nullity for Markov chains in bi-infinite random environments are firstly introduced,and their properties are discussed.Especially some criteria for states to be positive or null are given by making use of more powerful tools such as theories of invariant functions.