01319nas a2200157   4500000000100000000000100001008004100002260001200043100001700055700001700072700002200089700003200111245011100143490000700254520090000261       2020                            d  c11/20191 aDawid Czapla1 aSander Hille1 aKatarzyna Horbacz1 aHanna Wojewódka-Ściążko00aContinuous dependence of an invariant measure on the jump rate of a piecewise-deterministic Markov process0 v173 a<p>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 λ. 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,&nbsp;say ν_λ. The aim of this paper is to prove that the map λ↦ν_λ 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.</p>