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Title: Continuous dependence of an invariant measure on the jump rate of a piecewisedeterministic Markov process
Authors: Czapla, Dawid
Hille, Sander C.
Horbacz, Katarzyna
Wojewódka-Ściążko, Hanna
Keywords: invariant measure; piecewise-deterministic Markov process; random dynamical system; jump rte; continuous dependence
Issue Date: 2020
Citation: Mathematical Biosciences and Engineering, Vol. 17, Iss. 2 (2020), s. 1059–1073
Abstract: We investigate a piecewise-deterministic Markov process, evolving on a Polish metric space, whose deterministic behaviour between random jumps is governed by some semi-flow, and any state right after the jump is attained by a randomly selected continuous transformation. It is assumed that the jumps appear at random moments, which coincide with the jump times of a Poisson process with intensity . The model of this type, although in a more general version, was examined in our previous papers, where we have shown, among others, that the Markov process under consideration possesses a unique invariant probability measure, say . The aim of this paper is to prove that the map 7! is continuous (in the topology of weak convergence of probability measures). The studied dynamical system is inspired by certain stochastic models for cell division and gene expression.
DOI: 10.3934/mbe.2020056
ISSN: 1551-0018
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