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Rates of convergence of stochastically monotone and continuous time Markov models

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

G. O. Roberts  and
R. L. Tweedie
G. O. Roberts*
Affiliation:
University of Lancaster
R. L. Tweedie*
Affiliation:
School of Public Health, Minneapolis
*
∗Postal address: Department of Mathematics and Statistics, University of Lancaster, Lancaster LA1 4YF, England. Email address: [email protected].
∗∗Postal address: Division of Biostatistics, University of Minnesota, A460 Mayo Building, Box 303, 420 Delaware Street, SE Minneapolis, MN 55455-0378, USA. Email address: [email protected]
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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

Stochastic monotonicityrates of convergenceMarkov chainMarkov process

MSC classification

Primary: 60J05: Discrete-time Markov processes on general state spaces 60J25: Continuous-time Markov processes on general state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 2 , June 2000 , pp. 359 - 373
Copyright
Copyright © by the Applied Probability Trust 2000 

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Footnotes

Work supported in part by NSF Grant DMS 9803682 and EPSRC grant GR/J19900.

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