Weak Convergence of Obliquely Reflected Diffusions

TL;DR

This paper extends previous results on the weak convergence of reflected Brownian motions by analyzing obliquely reflected diffusion processes, requiring domain convergence stronger than Wijsman but weaker than Hausdorff topology.

Contribution

It generalizes the weak convergence results to obliquely reflected diffusions, broadening the scope beyond normally reflected Brownian motions.

Findings

Established weak convergence of obliquely reflected diffusions under domain convergence.

Identified the domain convergence condition as stronger than Wijsman topology.

Provided a framework for analyzing oblique reflections in diffusion processes.

Abstract

Burdzy and Chen (1998) proved results on weak convergence of multidimensional normally reflected Brownian motions. We generalize their work by considering obliquely reflected diffusion processes. We require weak convergence of domains, which is stronger than convergence in Wijsman topology, but weaker than convergence in Hausdorff topology.