Existence of invariant densities for semiflows with jumps

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:435

Article

Biedrzycka, Weronika¹  Tyran-Kaminska, Marta¹ 

[1] Univ Silesia, Inst Math, PL-40007 Katowice, Poland

关键词: Piecewise deterministic Markov process;    Stochastic semigroup;    Invariant density;    Dynamical systems with switching;    Gene expression models;   

DOI  :  10.1016/j.jmaa.2015.10.019

来源: Elsevier

【 摘 要 】

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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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