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

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

Michel Benaïm, Oliver Tough

Department of Mathematical Sciences

University of Neuchâtel

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Number of pages	42
Journal	Probability Theory and Related Fields
Early online date	12 Aug 2024
DOIs	https://doi.org/10.1007/s00440-024-01307-y
Publication status	E-pub ahead of print - 12 Aug 2024

Funding

The work of MB, and partially that of OT, was funded by the Grant 200020-219913 from the Swiss National Foundation. The work of OT was also partially funded by the EPSRC MathRad programme grant EP/W026899/. We thank two anonymous referees for their valuable comments and suggestions.

Funders	Funder number
Swiss National Science Foundation
Wellcome EPSRC Centre for Medical Engineering	EP/W026899/
Wellcome EPSRC Centre for Medical Engineering

Keywords

37
37C
60
60J

ASJC Scopus subject areas

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

Access to Document

10.1007/s00440-024-01307-yLicence: CC BY

Cite this

@article{0a686a49bab94c0780f2a37934af7cde,

title = "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.",

keywords = "37, 37C, 60, 60J",

author = "Michel Bena{\"i}m and Oliver Tough",

year = "2024",

month = aug,

day = "12",

doi = "10.1007/s00440-024-01307-y",

language = "English",

journal = "Probability Theory and Related Fields",

issn = "0178-8051",

publisher = "Springer New York",

}

TY - JOUR

T1 - On invariant distributions of Feller Markov chains with applications to dynamical systems with random switching

AU - Benaïm, Michel

AU - Tough, Oliver

PY - 2024/8/12

Y1 - 2024/8/12

N2 - 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.

AB - 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.

KW - 37

KW - 37C

KW - 60

KW - 60J

UR - http://www.scopus.com/inward/record.url?scp=85200977483&partnerID=8YFLogxK

U2 - 10.1007/s00440-024-01307-y

DO - 10.1007/s00440-024-01307-y

M3 - Article

AN - SCOPUS:85200977483

SN - 0178-8051

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

ER -

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

Abstract

Funding

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this