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Examples for the Theory of Strong Stationary Duality with Countable State Spaces

Published online by Cambridge University Press:  27 July 2009

Persi Diaconis  and
James Allen Fill
Persi Diaconis
Affiliation:
Department of MathematicsHarvard University Cambridge, Massachusetts 02138
James Allen Fill
Affiliation:
Department of Mathematical SciencesThe Johns Hopkins University Baltimore, Maryland 21218
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Abstract

Let X1,X2,… be an ergodic Markov chain on the countable state space. We construct a strong stationary dual chain X* whose first hitting times give sharp bounds on the convergence to stationarity for X. Examples include birth and death chains, queueing models, and the excess life process of renewal theory. This paper gives the first extension of the stopping time arguments of Aldous and Diaconis [1,2] to infinite state spaces.

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Type
Articles
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Probability in the Engineering and Informational Sciences , Volume 4 , Issue 2 , April 1990 , pp. 157 - 180
Copyright
Copyright © Cambridge University Press 1990

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