Rates of convergence of stochastically monotone and continuous time Markov models

In this paper we give bounds on the total variation distance from convergence of a continuous time positive recurrent Markov process on an arbitrary state space, based on Foster-Lyapunov drift and minorisation conditions. Considerably improved bounds are given in the stochastically monotone case, for both discrete and continuous time models, even in the absence of a reachable minimal element. These results are applied to storage models and to diffusion processes.

[1]  T. Lindvall.  Lectures on the Coupling Method , 1992 .

[2]  S. Meyn,et al.  Computable Bounds for Geometric Convergence Rates of Markov Chains , 1994 .

[3]  Vladimir Kalashnikov,et al.  Topics on Regenerative Processes , 1994 .

[4]  R. Tweedie,et al.  Bounds on regeneration times and convergence rates for Markov chains fn1 fn1 Work supported in part , 1999 .

[5]  R. L. Tweedie,et al.  Explicit Rates of Convergence of Stochastically Ordered Markov Chains , 1996 .

[6]  Richard L. Tweedie,et al.  Geometric Convergence Rates for Stochastically Ordered Markov Chains , 1996, Math. Oper. Res..

[7]  Gareth O. Roberts,et al.  Quantitative Bounds for Convergence Rates of Continuous Time Markov Processes , 1996 .

[8]  A. W. Kemp,et al.  Applied Probability and Queues , 1989 .

[9]  Jun S. Liu,et al.  Metropolized independent sampling with comparisons to rejection sampling and importance sampling , 1996, Stat. Comput..

[10]  V. Kalashnikov,et al.  Regeneration and general Markov chains , 1994 .

[11]  A. Borovkov.  Ergodicity and stability of stochastic processes , 1998 .

[12]  S. Meyn,et al.  Stability of Markovian processes III: Foster–Lyapunov criteria for continuous-time processes , 1993, Advances in Applied Probability.

[13]  J. Rosenthal.  Minorization Conditions and Convergence Rates for Markov Chain Monte Carlo , 1995 .

[14]  Jeffrey S. Rosenthal,et al.  Analysis of the Gibbs Sampler for a Model Related to James-stein Estimators , 2007 .

[15]  S. Meyn,et al.  Computable exponential convergence rates for stochastically ordered Markov processes , 1996 .

[16]  Richard L. Tweedie,et al.  Markov Chains and Stochastic Stability , 1993, Communications and Control Engineering Series.