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arXiv · 2102.12315

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

Michele Coghi·Wolfgang Dreyer·Paul Gajewski·Clemens Guhlke·Peter Friz·Mario Maurelli
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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.

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Michele Coghi, Wolfgang Dreyer, Paul Gajewski, Clemens Guhlke, Peter Friz, Mario Maurelli. 2021-02-24. A McKean-Vlasov SDE and particle system with interaction from reflecting boundaries. https://arxiv.org/abs/2102.12315

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