SDE with oblique reflection on domains defined by multiple constraints

TL;DR

This paper establishes conditions for the existence and uniqueness of solutions to reflected stochastic differential equations with multiple constraints, and explores their properties including time-reversibility and applications to particle clustering.

Contribution

It introduces simple assumptions ensuring unique strong solutions for SDEs with oblique reflection on complex domains and analyzes their reversibility and applications.

Findings

Unique strong solutions under simple assumptions

Time-reversibility for gradient systems with normal or fixed oblique reflection

Application to particle clustering around a large sphere

Abstract

We present simple assumptions on the constraints defining a hard core dynamics for the associated reflected stochastic differential equation to have a unique strong solution. Time-reversibility is proven for gradient systems with normal reflection, or oblique reflection with a fixed oblicity matrix. An application is given concerning the clustering at equilibrium of particles around a large attractive sphere.