Some simple but challenging Markov processes

Abstract

In this note, we present few examples of Piecewise Deterministic Markov Processes and their long time behavior. They share two important features: they are related to concrete models (in biology, networks, chemistry,...) and they are mathematically rich. Their mathematical study relies on coupling method, spectral decomposition, PDE technics, functional inequalities. We also relate these simple examples to recent and open problems.