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 obtained by random composition of maps and to piecewise deterministic Markov processes obtained by random switching between flows.

arXiv commentAn error in the statement of Theorem 2.11 has been corrected

References in corpus (5)

• Exponential ergodicity for Markov processes with random switching
• Invariant densities for dynamical systems with random switching
• Regularity of invariant densities for 1D-systems with random switching
• Smooth invariant densities for random switching on the torus
• Supports of Invariant Measures for Piecewise Deterministic Markov Processes