On the Markov commutator

Laurent Miclo ()
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Laurent Miclo: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique

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Abstract: The Markov commutator associated to a finite Markov kernel P is the convex semigroup consisting of all Markov kernels commuting with P. Its interest comes from its relation with the hypergroup property and with the notion of Markovian duality by intertwining. In particular, it is shown that the discrete analogue of the Achour-Trimèche's theorem, asserting the preservation of non-negativity by the wave equations associated to certain Metropolis birth and death transition kernels, cannot be extended to all convex potentials. But it remains true for symmetric and monotone potentials which are sufficiently convex.

Keywords: Symmetry group of a Markov kernel; Hypergroup property; Duality by intertwining; Birth and death chains; Metropolis algorithms; One-dimensional discrete wave equations (search for similar items in EconPapers)
Date: 2019-08
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Published in Bulletin des Sciences Mathématiques, 2019, vol. 154, pp.1-35

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-02476060

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