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Strong stationary duality for continuous-time Markov chains. Part I: Theory

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Abstract

LetX(t), 0≤t<∞, be an ergodic continuous-time Markov chain with finite or countably infinite state space. We construct astrong stationary dual chainX * whose first hitting times yield bounds on the convergence to stationarity forX. The development follows closely the discrete-time theory of Diaconis and Fill.(2,3) However, for applicability it is important that we formulate our results in terms of infinitesimal rates, and this raises new issues.

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Authors and Affiliations

  1. Department of Mathematical Sciences, The Johns Hopkins University, Baltimore, Maryland

    James Allen Fill

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  1. James Allen Fill
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Fill, J.A. Strong stationary duality for continuous-time Markov chains. Part I: Theory. J Theor Probab 5, 45–70 (1992). https://doi.org/10.1007/BF01046778

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  • DOI: https://doi.org/10.1007/BF01046778

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