Rates of convergence of stochastically monotone and continuous time Markov models
- 1 June 2000
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 37 (2) , 359-373
- https://doi.org/10.1239/jap/1014842542
Abstract
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.Keywords
This publication has 12 references indexed in Scilit:
- Bounds on regeneration times and convergence rates for Markov chainsStochastic Processes and their Applications, 1999
- Analysis of the Gibbs sampler for a model related to James-Stein estimatorsStatistics and Computing, 1996
- Geometric Convergence Rates for Stochastically Ordered Markov ChainsMathematics of Operations Research, 1996
- Computable exponential convergence rates for stochastically ordered Markov processesThe Annals of Applied Probability, 1996
- Quantitative Bounds for Convergence Rates of Continuous Time Markov ProcessesElectronic Journal of Probability, 1996
- Minorization Conditions and Convergence Rates for Markov Chain Monte CarloJournal of the American Statistical Association, 1995
- Computable Bounds for Geometric Convergence Rates of Markov ChainsThe Annals of Applied Probability, 1994
- Regeneration and general Markov chainsJournal of Applied Mathematics and Stochastic Analysis, 1994
- Topics on regenerative processesInternational Journal of Stochastic Analysis, 1994
- Markov Chains and Stochastic StabilityPublished by Springer Nature ,1993