Long time behavior of Markov processes

Abstract

These notes correspond to a three hours lecture given during the workshop “Metastability and Stochastic Processes”held in Marne-la-Vallée in September 21st-23rd 2011. I would like to warmly thank the organizers Tony Lelièvre and Arnaud Guillin for a very nice organization and for obliging me first to give the lecture, second to write these notes. I also want to acknowledge all the people who attended the lecture.