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. MaurelliUltimo
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.
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