On Martin Boundary In The Construction Theory Of Markov Chains

Martin effective exit boundary of minimal process is very important in the con-struction theory of Markov chains. In eference documentation [1],the author founded the excursion theory of Markov chains and gavegeneral methods to construct Markov chains.In eference documentation [1], the author showed that Martin effective exit boundary is dense in Ray-Knight compacttifiction of state space of a Markov chain, then Markov chain of finite Martin effective exit boundary is simple. In this paper we shall show that in the case that Martin effective exit boundary is infinite, Martin effective exit boundary may have other culminamt points.