Multiple Points Excursion Theory Of Markov Chains

For Markov chains with finite instanteneous states, it is very difficult to describe their path structures with Ito's excursion theory, even their equilibrium distributions. Generally, excursion outside instanteneous states are driven by its Q-matrices,and motions in instanteneous states are just Markov chains with finite states. In this paper, we use Ito's idea and Motoo's theory to describe path structures of Markov chains with finite instanteneous states, and give their boundary processes.