01339nas a2200145   4500000000100000000000100001008004100002260001200043100001700055700002200072700003200094245014700126490000800273520091200281       2022                            d  c02/20221 aDawid Czapla1 aKatarzyna Horbacz1 aHanna Wojewódka-Ściążko00aExponential ergodicity in the bounded-Lipschitz distance for some piecewise-deterministic Markov processes with random switching between flows0 v2133 a<p>&nbsp;In this paper, we study a subclass of piecewise-deterministic Markov processes with a Polish state space, involving deterministic motion punctuated by random jumps that occur at exponentially distributed time intervals. Over each of these intervals, the process follows a flow, selected randomly among a finite set of all possible ones. Our main goal is to provide a set of verifiable conditions guaranteeing the exponential ergodicity for such processes (in terms of the bounded Lipschitz distance), which would refer only to properties of the flows and the transition law of the Markov chain given by the post-jump locations. Moreover, we establish a simple criterion on the exponential ergodicity for a particular instance of these processes, applicable to certain biological models, where the jumps result from the action of an iterated function system with place-dependent probabilities.</p>