Georgia Institute of Technology College of Sciences

In my talk, I will present the main results of a recent article by Martin Hairer and Jonathan Mattingly on an ergodic theorem for Markov chains. I will consider Markov chains evolving in discrete time on an abstract, possibly uncountable, state space. Under certain regularity assumptions on the chain's transition kernel, such as the existence of a Foster-Lyapunov function with small level sets (what exactly is meant by that will be thoroughly explained in the talk), one can establish the existence and uniqueness of a stationary distribution. I will focus on a new proof technique for that theorem which relies on a family of metrics on the set of probability measures living on the state space. The main result of my talk will be a strict contraction estimate involving these metrics.