Wasserstein distance estimates for jump-diffusion processes

Abstract

We derive Wasserstein distance bounds between the probability distributions of a stochastic integral (Itô) process with jumps (Xt)t∈[0,T] and a jump-diffusion process (Xt∗)t∈[0,T]. Our bounds are expressed using the stochastic characteristics of (Xt)t∈[0,T] and the jump-diffusion coefficients of (Xt∗)t∈[0,T] evaluated in Xt, and apply in particular to the case of different jump characteristics. Our approach uses stochastic calculus arguments and Lp integrability results for the flow of stochastic differential equations with jumps, without relying on the Stein equation.