Wasserstein Convergence for Empirical Measures of Subordinated Diffusions on Riemannian Manifolds

Abstract

Let $M$ be a connected compact Riemannian manifold possibly with a boundary, let $V\in C^2(M)$ such that $μ(\d x):=\e^{V(x)}\d x$ is a probability measure, where $\d x$ is the volume measure, and let $L=\Delta +\nabla V$. The exact convergence rate in Wasserstein distance is derived for empirical measures of subordinations for the (reflecting) diffusion process generated by $L$.

26 pages