Journal of Applied Probability

Exact estimation for Markov chain equilibrium expectations

Peter W. Glynn and Chang-Han Rhee

Abstract

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.

Article information

Source
J. Appl. Probab. Volume 51A (2014), 377-389.

Dates
First available in Project Euclid: 2 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1417528487

Digital Object Identifier
doi:10.1239/jap/1417528487

Mathematical Reviews number (MathSciNet)
MR3317370

Zentralblatt MATH identifier
1312.65003

Subjects
Primary: 65C05: Monte Carlo methods
Secondary: 60J05: Discrete-time Markov processes on general state spaces

Keywords
Unbiased estimation Markov chain equilibrium expectation Markov chain stationary expectation exact estimation exact sampling exact simulation perfect sampling perfect simulation

Citation

Glynn, Peter W.; Rhee, Chang-Han. Exact estimation for Markov chain equilibrium expectations. J. Appl. Probab. 51A (2014), 377--389. doi:10.1239/jap/1417528487. https://projecteuclid.org/euclid.jap/1417528487.


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