A Class Of Markov Chains With Uni-instantaneous State

The Existence of Markov Chains with uni-instantaneous state are always a difficult part of theory of Markov processes. In this paper, we use excursion to get the necessary conditions of existence of Markov Chains with uni-instantaneous state, and use Motoo's theory to prove these conditions are sufficient conditions for existence of Markov Chains with uni-instantaneous state under summable case. Our results are extension of the classical results of Prof. Z. T. Hou and his students.