The Ergodicity Of Birth-death Processes With Single Instantaneous State

In this paper,we discuss the ergodicity of birth-death processes with single instantaneous state.We suppose its transition function is p_ij(t).Using the method of Ray-Knight and the excusion theory of Markov Process,we get the strong ergodicity of p_ij(t).Even more,we obtain the lower bound estimation of the maximum convergence speed of exponential ergodicity.