The Ergodicity Of Markov Chains Which Have Only One Instantaneous Points

In the theory of Markov processes,the construction of the sample paths of Markov chains is described clearly. One of the applications is that it completely describes the construction of Markov processes. We can obtain the resolvent of Markov chains by use of the formula of excursion. In this paper, I make use of the theory of excursion of Markov chains, I obtain stationary distribution of Markov chains from the construction of Markov chains, so I can judge the ergodicity of Markov chains which have instantaneous points,then deal with especial state, finally I obtain exponentially ergodicity of Markov chains which have instaneous points. In this paper, I make an example of birth and death process which have instaneous points.