Run Theory That The Only Criterion For Q Process

Markov process theorem is an important random process in the field of probability. The former model is the Markov chains which was introduced by Markov.A.A in 1907.The uniqueness and existeness of Constitution Theorem was called the Q -Matrix problem by D.Williams . Four sections constitute this paper.In the first chapter, we simply introduce the history and the present conditions of the Markov process, and we especially pay more attention to the problems of Q -matrix. By reading this chapter, we can generally understand the Markov process and Q -process; furthermore, we can also know how to study the uniqueness of the Q -process from another respect.In the second chapter, we outline the knowledge which will be used in the following chapter. First of all, we introduce a concept called Ray-Knight to constitute a Ray space. Then we induce a random variation {X_t} which has some characteristics of Markov process on this space.In the third chapter, we point out a concept of Local times, and then induce the concept of excursion. At last, we know the characteristics of Markov chains which lies on the point of S_∞.In the fourth chapter, firstly we give a concept of excursion measures by the random process {X_t}and the Local time at the point S_∞. Then we introduce the concept of incursion system. Based on the above, we prove the uniqueness of Q -process at last.