The Recurrence And Transience Of Markov Chains As Well As The Existence Of Invariant Measures

In this article we use Markov chains with an atom for the basis, then search the recurrence and transience of irreducible chains as well an the existence of invariant measures of recurrent chains,and construct the invariant measures。 we also discuss the relationship between the recurrence and Harris recurrence、 positive recurrence and regularity.this article is composed of four parts:In the first part, we briefly introduce the background of Markov chains and the contents of this thesis.In the second part, we recall the basic knowledge of Markov chains,which in-clude the basic properties and theorems.we use these properties and theorems to give another judgment method of the recurrence and transience.In the third part, we recall the basic knowledge of invariant measures and discuss the existence of invariant measures of recurrent chains.In the fourth part, we recalled some concepts in part2and part3, Now we discuss the relationship between them.