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 / M. Coghi, W. Dreyer, P.K. Friz, P. Gajewski, C. Guhlke, M. Maurelli. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 54:2(2022), pp. 2251-2294. [10.1137/21M1409421]

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

M. Maurelli
Ultimo
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.
McKean--Vlasov SDEs; mean-field interacting diffusions; reflecting boundaries;
Settore MAT/06 - Probabilita' e Statistica Matematica
2022
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/925652
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