Free-transport equation with boundary effects and sub-geometric convergence to equilibrium of Markov processes

In this talk, I will present a study of the long-time behavior of a model from kinetic theory introduced by Aoki & Golse, in which particles travel with no interactions in a bounded domain until they hit the frontier.
The corresponding Markov process is an instance of the class of Markov processes with sub-geometric convergence, about which a lot of understanding has been gained during the last 15 years. I will present a first way to derive some results on the model based on a coupling method, and then discuss the general theory of Markov processes with sub-geometric convergence, as well as some recent developments.