Author:
Diaconis Persi,Fill James Allen
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.
Publisher
Cambridge University Press (CUP)
Subject
Industrial and Manufacturing Engineering,Management Science and Operations Research,Statistics, Probability and Uncertainty,Statistics and Probability
Reference22 articles.
1. Fill J.A. (1990a). Strong stationary duality for continuous-time Markov chains. Unpublished manuscript.
2. Honest Bernoulli excursions;Diaconis;Advances in Applied Probability,1988
3. Diaconis P. & Fill J.A. (1990). Strong stationary times via a new form of duality. Annals of Probability in press.
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