Wasserstein distance on solutions to stochastic differential equations with jumps

Abstract

In this paper, we shall focus on the Wasserstein distance between two jump processes determined by stochastic differential equations in $\mathbb{R}^d$ or the Riemannian manifold $M$. As an application, the study on the Wasserstein distance implies that the law of the subordinated Brownian motion on $M$ is different from the one of the canonical projected process of the Marcus-type equation with jumps valued in the bundle of orthonormal frames $O(M)$.