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 / Coghi, M.; Dreyer, W.; Friz, P. K.; Gajewski, P.; Guhlke, C.; Maurelli, M.. - 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
Coghi M.;
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.| File | Dimensione | Formato | |
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