On Markov Intertwining Relations and Primal Conditioning

Marc Arnaudon (), Koléhè Coulibaly-Pasquier () and Laurent Miclo ()
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Marc Arnaudon: Université de Bordeaux, CNRS, Bordeaux INP, IMB
Koléhè Coulibaly-Pasquier: Université de Lorraine and CNRS
Laurent Miclo: Esplanade de l’université

Journal of Theoretical Probability, 2024, vol. 37, issue 3, 2425-2456

Abstract: 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.

Keywords: Algebraic and probabilistic Markov intertwining relations; Subset conditioning; Doob transform; Discrete Pitman intertwining; Top-to-random shuffle; Birth-and-death Markov chains; Strong stationary times; Primary 60J10; Secondary 15B51 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-023-01301-5

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