Speaker
Description
In this talk, relying on Foster-Lyapunov drift conditions, we will discuss subexponential upper and lower bounds on the rate of convergence in the Lp-Wasserstein distance for a class of irreducible and aperiodic Markov processes. We will further discuss these results in the context of Markov Lévy-type processes. In the lack of irreducibility and/or aperiodicity properties, we will comment on exponential ergodicity in the Lp-Wasserstein distance for a class of Ito processes under an asymptotic flatness (uniform dissipativity) assumption. Lastly, applications of these results to specific processes will be presented, including Langevin tempered diffusion processes, piecewise Ornstein–Uhlenbeck processes with jumps under constant and stationary Markov controls, and backward recurrence time chains, for which we will provide a sharp characterization of the rate of convergence via matching upper and lower bounds.
