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Strong Stationary Times Via a New Form of Duality

Persi Diaconis and James Allen Fill
The Annals of Probability
Vol. 18, No. 4 (Oct., 1990), pp. 1483-1522
Stable URL: http://www.jstor.org/stable/2244330
Page Count: 40
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Strong Stationary Times Via a New Form of Duality
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Abstract

A strong stationary time for a Markov chain (Xn) is a stopping time T for which XT is stationary and independent of T. Such times yield sharp bounds on certain measures of nonstationarity for X at fixed finite times n. We construct an absorbing dual Markov chain with absorption time a strong stationary time for X. We relate our dual to a notion of duality used in the study of interacting particle systems. For birth and death chains, our dual is again birth and death and permits a stochastic interpretation of the eigenvalues of the transition matrix for X. The duality approach unifies and extends the analysis of previous constructions and provides several new examples.

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