Ergodicity Estimation Of General Birth-death Processes

Ergodicity is key problem of Markov processes and attracts many probabilitier.Birth-death processes are most simple Markov processes and their ergodicity is very complete under the condition that they satisfy the uniqueness condition.In this paper we prove that the birth-death processes are exponential ergodic under the condition that ? is exit and enter,and give some estaimate of their maximal ergodicity.