On invariant distributions of Feller Markov chains with applications to dynamical systems with random switching

Abstract We introduce simple conditions ensuring that invariant distributions of a Feller Markov chain on a compact Riemannian manifold are absolutely continuous with a lower semi-continuous, continuous or smooth density with respect to the Riemannian measure. This is applied to Markov chains obtain...

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Bibliographic Details
Published inProbability theory and related fields
Main Authors Benaïm, Michel, Tough, Oliver
Format Journal Article
LanguageEnglish
Published 12.08.2024
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Summary:Abstract We introduce simple conditions ensuring that invariant distributions of a Feller Markov chain on a compact Riemannian manifold are absolutely continuous with a lower semi-continuous, continuous or smooth density with respect to the Riemannian measure. This is applied to Markov chains obtained by random composition of maps and to piecewise deterministic Markov processes obtained by random switching between flows.
ISSN:0178-8051
1432-2064
DOI:10.1007/s00440-024-01307-y