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Convergence Properties of Perturbed Markov Chains

Part of: Parametric inference Inference from stochastic processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Gareth O. Roberts ,
Jeffrey S. Rosenthal  and
Peter O. Schwartz
Gareth O. Roberts*
Affiliation:
University of Cambridge
Jeffrey S. Rosenthal*
Affiliation:
University of Toronto
Peter O. Schwartz*
Affiliation:
University of Toronto
*
∗Postal address: Statistical Laboratory, University of Cambridge, Cambridge CB2 1SB, UK. e-mail address: [email protected]
∗∗Postal address: Department of Statistics, University of Toronto, Toronto, Ontario, Canada M5S 1A1. e-mail address: [email protected]
∗∗∗Postal address: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 1A1. e-mail address: [email protected]
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Abstract

In this paper, we consider the question of which convergence properties of Markov chains are preserved under small perturbations. Properties considered include geometric ergodicity and rates of convergence. Perturbations considered include roundoff error from computer simulation. We are motivated primarily by interest in Markov chain Monte Carlo algorithms.

Keywords

Markov chainMonte Carloperturbationroundoff errorgeometric convergenceconvergence rate

MSC classification

Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 62F99: None of the above, but in this section 62M05: Markov processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 1 , March 1998 , pp. 1 - 11
Copyright
Copyright © Applied Probability Trust 1998 

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