Ray-Knight Compactification Of Markov Chain

A Markov chain whose the problem of the construction is a big problem that is not tackled easily.Because a general Markov chain has only locally strong Markov property .The key of solving the big problem is to structure a Markov chain with the strong Markov property. This article tells us how to structure a Markov chain with the strong Markov property in a general discrete state space E,to use the " resolvent property " and to take the " Ray-Knight compactification " of the state space E as a bridge.First,it intruduces some elementary concepts and assumptions;Second,it elaborates particular the " Ray-Knight compactification " from analysis's angle;Third,it tells us how to structure a Markov chain with the strong Markov property from the probability angle.