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

Michel Benaïm; Oliver Tough

doi:10.1007/s00440-024-01307-y

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arXiv · 2310.17543

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

Michel Benaïm·Oliver Tough

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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.

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BibTeX RIS

Michel Benaïm, Oliver Tough. 2023-10-26. On invariant distributions of Feller Markov chains with applications to dynamical systems with random switching. https://doi.org/10.1007/s00440-024-01307-y

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