Particle Approximation of the Wasserstein Diffusion

TL;DR

This paper constructs a particle system of Bessel processes on the interval that converges to the Wasserstein Diffusion, providing a new approximation method under certain mathematical conditions.

Contribution

It introduces a novel particle approximation scheme for Wasserstein Diffusion using interacting Bessel processes, with convergence proven via Dirichlet form analysis.

Findings

Empirical measure process converges to Wasserstein Diffusion

Convergence relies on Markov uniqueness assumption

Uses variational convergence of Dirichlet forms in Mosco sense

Abstract

We construct a system of interacting two-sided Bessel processes on the unit interval and show that the associated empirical measure process converges to the Wasserstein Diffusion, assuming that Markov uniqueness holds for the generating Wasserstein Dirichlet form. The proof is based on the variational convergence of an associated sequence of Dirichlet forms in the generalized Mosco sense of Kuwae and Shioya.