01272nas a2200157   4500000000100000000000100001008004100002260001200043100001700055700001700072700002200089700003200111245016200143490000700305520080200312       2021                            d  c09/20201 aDawid Czapla1 aSander Hille1 aKatarzyna Horbacz1 aHanna Wojewódka-Ściążko00aThe law of the iterated logarithm for a piecewise deterministic Markov process assured by the properties of the Markov chain given by its post-jump locations0 v393 a<p>In the paper, we consider some piecewise deterministic Markov process, whose continuous component evolves according to semiflows, which are switched at the jump times of a Poisson process. The associated Markov chain describes the states of this process directly after the jumps. Certain ergodic properties of these two dynamical systems have been already investigated in our recent papers. We now aim to establish the law of the iterated logarithm for the aforementioned continuous-time process. Moreover, we intend to do this using the already proven properties of the discrete-time system. The abstract model under consideration has interesting interpretations in real-life sciences, such as biology. Among others, it can be used to describe the stochastic dynamics of gene expression.</p>