On Markov intertwining relations and primal conditioning
Résumé
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-torandom shuffle and absorbed birth-and-death chain intertwinings serve as illustrations.
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