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Perturbation bounds for the stationary probabilities of a finite Markov chain

Published online by Cambridge University Press:  01 July 2016

Moshe Haviv  and
Ludo Van Der Heyden
Moshe Haviv*
Affiliation:
Hebrew University, Jerusalem
Ludo Van Der Heyden*
Affiliation:
Yale University
*
∗Postal address: Department of Statistics, Hebrew University, Jerusalem 91905, Israel.
∗∗ Postal address: School of Organization and Management, Yale University, New Haven, CT 06520, USA.
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Abstract

This paper discusses perturbation bounds for the stationary distribution of a finite indecomposable Markov chain. Existing bounds are reviewed. New bounds are presented which more completely exploit the stochastic features of the perturbation and which also are easily computable. Examples illustrate the tightness of the bounds and their application to bounding the error in the Simon–Ando aggregation technique for approximating the stationary distribution of a nearly completely decomposable Markov chain.

Keywords

NEARLY COMPLETELY DECOMPOSABLE SYSTEMSSTOCHASTIC MATRICES
Type
Research Article
Information
Advances in Applied Probability , Volume 16 , Issue 4 , December 1984 , pp. 804 - 818
Copyright
Copyright © Applied Probability Trust 1984 

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