On absolute continuity of invariant measures associated with a piecewise-deterministic Markov process with random switching between flows

TytułOn absolute continuity of invariant measures associated with a piecewise-deterministic Markov process with random switching between flows
Publication TypeJournal Article
Rok publikacji2021
AutorzyCzapla D, Horbacz K, Wojewódka-Ściążko H
JournalNonlinear Analysis
Volume213
Start Page112522
Date Published12/2021
Słowa kluczoweabsolute continuity, ergodic measure, invariant measure, piecewise-deterministic Markov process, singularity, switching semiflows
Abstract

We are concerned with the absolute continuity of stationary distributions corresponding to some piecewise deterministic Markov process, being typically encountered in biological models. The process under investigation involves a deterministic motion punctuated by random jumps, occurring at the jump times of a Poisson process. The post-jump locations are obtained via random transformations of the pre-jump states. Between the jumps, the motion is governed by continuous semiflows, which are switched directly after the jumps. The main goal of this paper is to provide a set of verifiable conditions implying that any invariant distribution of the process under consideration that corresponds to an ergodic invariant measure of the Markov chain given by its post-jump locations has a density with respect to the Lebesgue measure.

DOI10.1016/j.na.2021.112522