Date: Wednesday 5 March at 3PM
Title: Asymptotically Optimal Coupling of Lévy processes
Abstract: I will describe two couplings for Lévy processes that use the Poisson structure of jumps and the exchangeability of the increments of a Lévy process. As an application, we will see that these couplings are asymptotically optimal for stable processes in the small-time domain of attraction, wherein Berry-Esseen-type results and other standard tools fail to give convergence rates. We will also discuss lower bounds on these distances and establish the slow convergence for the non-normal domain of attraction.