Mufa, Chen, Exponential L²-Convergence and L²-Spectral Gap for Markov Processes, Acta Mathematica Sinica, New Series Chinese Journal of Mathematics, 7(1), 1991, pp. 19-37
This paper deals with the exponential L²-convergence for jump processes. We introduce some reduction methods and improve some previous results. Then we prove that for birth-death processes.expone ntial convergence coincides indeed with exponential ergodicity which is widely studied in the Markov chain theory.