Martin Boundary And The Number Of Transient Tense Of Markov Chain

Markov chain which is accompanied with transient tense is always the tricky problem of Markov chain, and its existence and uniqueness is also complicated. So far, the existence of the added case of Markov chain which is accompanied with transient tense has not been resolved. Because, dealing with the problem, ChangSha school which is led by professor HouZhenting who always use analysis and decomposition of limited dimension theorem, so, it is difficult to see the probability structure of the Markov chain which is accompanying with transient tense from their results. In this paper I have proved that the number of the transient tense which is accompanying with Markov chain Cannot exceed the number of its Martin positive outflow boundary using Ray-Knight method. Thus we have promoted the conclusion of the situation with limited transient tense.