Probalistic and piecewise deterministic models in biology

International audienceWe present recent results on Piecewise Deterministic Markov Processes (PDMPs), involved in biological modeling. PDMPs, first introduced in the probabilistic literature by [30], are a very general class ofMarkov processes and are being increasingly popular in biological applications. They also give new interest-ing challenges from the theoretical point of view. We give here different examples on the long time behaviorof switching Markov models applied to population dynamics, on uniform sampling in general branching mod-els applied to structured population dynamic, on time scale separation in integrate-and-fire models used in neuroscience, and, finally, on moment calculus in stochastic models of gene expression