01070nas a2200145   4500000000100000000000100001008004100002260001200043100001700055700002200072700003200094245011600126490000800242520067400250       2020                            d  c05/20201 aDawid Czapla1 aKatarzyna Horbacz1 aHanna Wojewódka-Ściążko00aErgodic properties of some piecewise-deterministic Markov process with application to gene expression modelling0 v1303 a<p>We investigate a piecewise-deterministic Markov process with a Polish state space, whose deterministic behaviour between random jumps is governed by a finite number of semiflows. We provide tractable conditions ensuring a form of exponential ergodicity and the strong law of large numbers for the chain given by the post-jump locations. Further, we establish a one-to-one correspondence between invariant measures of the chain and those of the continuous-time process. These results enable us to derive the strong law of large numbers for the latter. The studied dynamical system is inspired by certain models of gene expression, which are also discussed here.</p>