There has been considerable recent work on the problem of determinig, in some computable way, the rate of convergence of Markov chains and processes. Firstly, the authors develop continuous time results which are analogues of those from an earlier work by the authors [Stochastic Processes Appl. 80, No. 2, 211-229 (1999; Zbl 0961.60066)]. Secondly, the authors produce much sharper bounds in a specific class of models where Foster-Lyapunov techniques are particulary effective, namely when the Markov chain or process is stochastically monotone.
For related papers see V. V. Kalashnikov [J. Appl. Math. Stochastic Anal. 7, No. 3, 357-371 (1994; Zbl 0835.60059)], S. P. Meyn and R. L. Tweedie [Ann. Appl. Probab. 4, No. 4, 981-1011 (1994; Zbl 0812.60059)] and J. S. Rosenthal [J. Am. Stat. Assoc. 90, No. 430, 558-566 (1995; Zbl 0824.60077)].