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

• 成果类型: Article
• 署名作者: Benaim, Michel; Tough, Oliver
• 署名单位: University of Neuchatel; University of Bath
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-024-01307-y
• 发表日期: 2025
• 页码: 1283-1324
• 关键词: densities

摘要

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.