The Martin Boundary Of Minimal Processes And Ray-Knight Compactification

The Martin boundary of minimal processes and Ray-Knight compactification are two important content in Markov processes. They play an important role in constructions of Markov chains. But there is nobody who has done any research on their relations so far. In this paper we concentrate on studying partial relations between the Martin boundary of minimal processes and Ray-Knight compactification under the honest minimal transition function, and mainly obtain the bijective mapping between the Martin entrance boundary B_e of minimal processes and E~+\E in Ray-Knight compactification when E~+\E is finite.