A McKean-Vlasov SDE and particle system with interaction from reflecting boundaries

TL;DR

This paper studies a one-dimensional McKean-Vlasov stochastic differential equation with boundary reflection and a mean-field particle system, establishing well-posedness and convergence results despite the non-local reflection effects.

Contribution

It introduces a novel combination of boundary reflection and mean-field interaction in McKean-Vlasov SDEs, proving well-posedness and particle system convergence.

Findings

Pathwise well-posedness of the McKean-Vlasov SDE.

Convergence of the particle system as particle number grows.

Handling of non-local reflection effects in the analysis.

Abstract

We consider a one-dimensional McKean-Vlasov SDE on a domain and the associated mean-field interacting particle system. The peculiarity of this system is the combination of the interaction, which keeps the average position prescribed, and the reflection at the boundaries; these two factors make the effect of reflection non local. We show pathwise well-posedness for the McKean-Vlasov SDE and convergence for the particle system in the limit of large particle number.