Ito Excursion And Egodicity Of A Singular Makov Chain

This paper discusses egodicity of a singular markov chain by Ito excursion,and gives convergence bound of exponential ergodicity.First,we research the Ray-Knight of Markov chains in order to get the property and definition of leave∞excursion.Then,we use the excurison and Poisson process to research the ergodicity of Markov chains.In this paper,the convergence bound of this markov chains relay on its excursion anλsatisfied with Eⁱ[e^λσ_j]＜∞.