Existence of invariant densities for semiflows with jumps

DOI10.1016/J.JMAA.2015.10.019zbMATH Open1339.60107arXiv1510.03633OpenAlexW2190875877WikidataQ105583674 ScholiaQ105583674MaRDI QIDQ892307

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Publication date: 18 November 2015

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Abstract: The problem of existence and uniqueness of absolutely continuous invariant measures for a class of piecewise deterministic Markov processes is investigated using the theory of substochastic semigroups obtained through the Kato--Voigt perturbation theorem on the

L^{1}

-space. We provide a new criterion for the existence of a strictly positive and unique invariant density for such processes. The long time qualitative behavior of the corresponding semigroups is also considered. To illustrate our general results we give a detailed study of a two dimensional model of gene expression with bursting.

Full work available at URL: https://arxiv.org/abs/1510.03633

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