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 nonlocal. We show pathwise well-posedness for the McKean--Vlasov SDE and convergence for the particle system in the limit of large particle number.

A McKean--Vlasov SDE and Particle System with Interaction from Reflecting Boundaries

Maurelli, Mario
2022

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 nonlocal. We show pathwise well-posedness for the McKean--Vlasov SDE and convergence for the particle system in the limit of large particle number.
Coghi, Michele; Dreyer, Wolfgang; Friz, Peter K.; Gajewski, Paul; Guhlke, Clemens; Maurelli, Mario
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/1149879
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