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

Abstract

We consider a one-dimensional McKean-Vlasov SDE on a domain and the associated meanfield 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.