Wasserstein convergence of penalized Markov processes

by Edouard Strickler

Tuesday Nov 19, 2024, 9:50 AM → 10:50 AM Europe/Paris

Amphi Schwartz

We consider a Markov process living in some space E, and killed (penalized) at a rate depending on its position. In the last decade, several conditions have been given  ensuring that the law of the process conditioned on survival converges to a quasi-stationary distribution. When one of these conditions is satisfied, the convergence holds exponentially fast in total variation distance. In this talk, we will present very simple examples of penalized Markov processes whose conditional law cannot converge in total variation, and we will give a sufficient condition implying contraction and convergence of the conditional law in Wasserstein distance. We then apply this criterion to a collection of examples. This is a joint work with Nicolas Champagnat (Inria Nancy) and Denis Villemonais (Université de Strasbourg)