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On Markov Intertwining Relations and Primal Conditioning

Author

Listed:
  • Marc Arnaudon

    (Université de Bordeaux, CNRS, Bordeaux INP, IMB)

  • Koléhè Coulibaly-Pasquier

    (Université de Lorraine and CNRS)

  • Laurent Miclo

    (Esplanade de l’université)

Abstract

Given an intertwining relation between two finite Markov chains, we investigate how it can be transformed by conditioning the primal Markov chain to stay in a proper subset. A natural assumption on the underlying link kernel is put forward. The three classical examples of discrete Pitman, top-to-random shuffle and absorbed birth-and-death chain intertwinings serve as illustrations.

Suggested Citation

  • Marc Arnaudon & Koléhè Coulibaly-Pasquier & Laurent Miclo, 2024. "On Markov Intertwining Relations and Primal Conditioning," Journal of Theoretical Probability, Springer, vol. 37(3), pages 2425-2456, September.
    • Handle: RePEc:spr:jotpro:v:37:y:2024:i:3:d:10.1007_s10959-023-01301-5
    DOI: 10.1007/s10959-023-01301-5
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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. "On Hitting Times and Fastest Strong Stationary Times for Skip-Free and More General Chains," Journal of Theoretical Probability, Springer, vol. 22(3), pages 587-600, September.
    3. 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.
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