The Fundamental Theorem And The Application Of Markov Chains

In this paper, we mainly research the fundamental theorem and the applica-tion of markov chains. First, we introduce the existence theorem of markov chains and the positive small set existence theorem of φ-irreducible chain. Next, we in-troduce the period of markov chains and the minorization condition holds for m-skeleton. Then, we discuss in general state space, the petite sets forming the count-able cover.Finally, we study split chain and analyze the connecting between the split and original chains.The splitting construction is valuable because of the various proper-ties that Φ inherits from Φ.