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Strong Stationary Duality for Diffusion Processes

Author

Listed:
  • James Allen Fill

    (The Johns Hopkins University)

  • Vince Lyzinski

    (The Johns Hopkins University Human Language Technology Center of Excellence)

Abstract

We develop the theory of strong stationary duality for diffusion processes on compact intervals. We analytically derive the generator and boundary behavior of the dual process and recover a central tenet of the classical Markov chain theory in the diffusion setting by linking the separation distance in the primal diffusion to the absorption time in the dual diffusion. We also exhibit our strong stationary dual as the natural limiting process of the strong stationary dual sequence of a well-chosen sequence of approximating birth-and-death Markov chains, allowing for simultaneous numerical simulations of our primal and dual diffusion processes. Lastly, we show how our new definition of diffusion duality allows the spectral theory of cutoff phenomena to extend naturally from birth-and-death Markov chains to the present diffusion context.

Suggested Citation

  • James Allen Fill & Vince Lyzinski, 2016. "Strong Stationary Duality for Diffusion Processes," Journal of Theoretical Probability, Springer, vol. 29(4), pages 1298-1338, December.
    • Handle: RePEc:spr:jotpro:v:29:y:2016:i:4:d:10.1007_s10959-015-0612-1
    DOI: 10.1007/s10959-015-0612-1
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    References listed on IDEAS

    as
    1. Persi Diaconis & Laurent Miclo, 2009. "On Times to Quasi-stationarity for Birth and Death Processes," Journal of Theoretical Probability, Springer, vol. 22(3), pages 558-586, September.
    2. James Allen Fill, 2009. "The Passage Time Distribution for a Birth-and-Death Chain: Strong Stationary Duality Gives a First Stochastic Proof," Journal of Theoretical Probability, Springer, vol. 22(3), pages 543-557, September.
    Full references (including those not matched with items on IDEAS)

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