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The censored Markov chain and the best augmentation

Part of: Combinatorial probability

Published online by Cambridge University Press:  14 July 2016

Y. Quennel Zhao  and
Danielle Liu
Y. Quennel Zhao*
Affiliation:
University of Winnipeg
Danielle Liu
Affiliation:
Case Western Reserve University
*
∗Postal address: Department of Mathematics and Statistics, University of Winnipeg, Winnipeg, Manitoba, Canada R3B 2E9.
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Abstract

Computationally, when we solve for the stationary probabilities for a countable-state Markov chain, the transition probability matrix of the Markov chain has to be truncated, in some way, into a finite matrix. Different augmentation methods might be valid such that the stationary probability distribution for the truncated Markov chain approaches that for the countable Markov chain as the truncation size gets large. In this paper, we prove that the censored (watched) Markov chain provides the best approximation in the sense that, for a given truncation size, the sum of errors is the minimum and show, by examples, that the method of augmenting the last column only is not always the best.

Keywords

CENSORED MARKOV CHAINAUGMENTATIONSSTATIONARY PROBABILITIES

MSC classification

Primary: 60C05: Combinatorial probability
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 3 , September 1996 , pp. 623 - 629
Copyright
Copyright © Applied Probability Trust 1996 

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Footnotes

∗∗

Current address: AT&T Bell Laboratories, Holmdel, NJ 07733–3030, USA.

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