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Exact estimation for Markov chain equilibrium expectations

Part of: Probabilistic methods, simulation and stochastic differential equations Markov processes

Published online by Cambridge University Press:  30 March 2016

Peter W. Glynn  and
Chang-Han Rhee
Peter W. Glynn
Affiliation:
Management Science and Engineering, Stanford University, Stanford, CA 94305-4121, USA. Email address: glynn@stanford.edu.
Chang-Han Rhee
Affiliation:
Biomedical Engineering, Georgia Institute of Technology, U. A. Whitaker Building, 313 Ferst Drive, Atlanta, GA 30332, USA. Email address: rhee@gatech.edu.
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Abstract

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We introduce a new class of Monte Carlo methods, which we call exact estimation algorithms. Such algorithms provide unbiased estimators for equilibrium expectations associated with real-valued functionals defined on a Markov chain. We provide easily implemented algorithms for the class of positive Harris recurrent Markov chains, and for chains that are contracting on average. We further argue that exact estimation in the Markov chain setting provides a significant theoretical relaxation relative to exact simulation methods.

Keywords

Unbiased estimationMarkov chain equilibrium expectationMarkov chain stationary expectationexact estimationexact samplingexact simulationperfect samplingperfect simulation

MSC classification

Primary: 65C05: Monte Carlo methods
Secondary: 60J05: Discrete-time Markov processes on general state spaces
Type
Part 8. Markov processes and renewal theory
Information
Journal of Applied Probability , Volume 51 , Issue A: Celebrating 50 Years of The Applied Probability Trust , December 2014 , pp. 377 - 389
Copyright
Copyright © Applied Probability Trust 2014 

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