The Finite-dimension Decomposition Theorem

This paper includes the following two parts: In part one the anther introduce mainly some signals ,definitions and theorems; there are the content and the proof of the finite-dimension decomposition theorem in part two. For the problem of the resolvent's decomposition, Professor Hou discussed it in details in the Book of Q-Matrix problem of Markov Processes and proved it in the analytical way; In addition, Minoru Motoo applied additive functionals to the boundary problem of Markov processes and decomposed the resolvent in the paper of application of additive functionals to the boundary problem of Markov processes. In this paper the author decompose the resolvent by the use of the boundary process and excursion measure. Therefore, it's very easy to see it's probabihtical meaning. The important of this theorem is ont in itself; but it's one of the effective tools in the constructive theory for Markov Processes.