  We present recent results on Piecewise Deterministic Markov Processes
(PDMPs), involved in biological modeling. PDMPs, first introduced in the
probabilistic literature by Davis (1984), are a very general class of Markov
processes and are being increasingly popular in biological applications. They
also give new interesting challenges from the theoretical point of view. We
give here different examples on the long time behavior of switching Markov
models applied to population dynamics, on uniform sampling in general branching
models 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.
