The classification of states for Markov chain in random environments and m-irreducible
Weigang Wang, Dihe Hu · Wuhan University Journal of Natural Sciences · 2007
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.