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arXiv · 2004.06798

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

Dawid Czapla·Katarzyna Horbacz·Hanna Wojewódka-Ściążko
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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.

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Dawid Czapla, Katarzyna Horbacz, Hanna Wojewódka-Ściążko. 2020-04-14. On absolute continuity of invariant measures associated with a piecewise-deterministic Markov processes with random switching between flows. https://doi.org/10.1016/j.na.2021.11252

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