Coupling, ergodicity and transportation inequalities for SDEs with jumps

We present a construction of a coupling of solutions to a certain class of SDEs with jumps, which includes SDEs driven by symmetric $\alpha$-stable processes with $\alpha \in (1,2)$. As an application, we quantify the speed of convergence of solutions to such equations to their invariant measures, both in the standard $L^1$-Wasserstein and the total variation distances. As a second application, we obtain some transportation inequalities, which characterize concentration of the distributions of these solutions, and which were previously known only under the global dissipativity assumption on the drift.Non UBCUnreviewedAuthor affiliation: University of BonnGraduat