Speaker: Mateus Majka (Heriot-Watt University in Edinburgh.)
Title: Coupling, ergodicity and propagation of chaos for McKean-Vlasov SDEs with Lévy noise

Abstract: In this talk we are concerned with stochastic differential equations (SDEs) of McKean-Vlasov type, driven by d-dimensional Lévy processes.  We will present a construction of a coupling of solutions to such SDEs, and then we will apply it to study their convergence rates to stationary distributions. We will also consider a propagation of chaos result that explains how such SDEs can be approximated by interacting particle systems driven by independent Lévy processes. The presented approach, unlike more traditional methods, allows us to obtain explicit sharp bounds on convergence rates measured in Wasserstein distances. Based on joint work with Mingjie Liang (Sanming University, China) and Jian Wang (Fujian Normal University, China).