The Definition Of Markov Chain, The Property And Application Of Petiteness

The definition and irreducibility of Markov Chain,split chain,small set and petite set are the most basic theory of Markov Chains.It plays a fundamental role in the re-search of Markov Chain, also small set and petite set are the basic of the discussion of Markov Chain defined in the topological space. The first part of the article discusses the definition and existence theorem of Markov Chain, the maximal irreducible mea-sure. The second part,we discuss the property of split chain,The third part gives the discussion of the small set and petite set.