First of all,we introduces the concept of m-irreducible of Markov chain in random environment. Then under the condition of m-irreducible,the relationship of recurrent and positive recurrent between two states is studied. We also give several conditions that can imply a state is recurrent and positive recurrent. And then the period of a state is discussed and we obtained that under the condition of m-irreducible,for any two states in X ,they have the same period.
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