A note on absolute continuity of stationary distributions of some piecewise-deterministic Markov process

TitleA note on absolute continuity of stationary distributions of some piecewise-deterministic Markov process
Publication TypeBook Chapter
Year of Publication2022
AuthorsCzapla D, Horbacz K, Wojewódka-Ściążko H
Book TitleInternational Conference of Numerical Analysis and Applied Mathematics 2020 (ICNAAM 2020)
Volume2425
Series Volume420015
PublisherAIP Publishing
CityMelville, New York
ISBN Number978-0-7354-4182-8
Abstract

A piecewise deterministic Markov process with random switching between flows, occuring e.g. in certain stochastic models for gene expression, is considered in this article. The main goal is to provide a set of reasonable conditions under which any stationary distribution of the process that corresponds to an ergodic stationary distribution of the discrete-time Markov chain given by the post-jump locations of this process has a density with respect to the Lebesgue measure.

DOI10.1063/5.0081329