Pathwise Regularisation of McKean--Vlasov Equations

schedule le lundi 04 mai 2020 de 17h00 à 18h00

Organisé par : F. Bechtold, W. Da Silva , A. Fermanian, S. Has, Y. Yu

Intervenant : Avi Mayorcas (Oxford)
Lieu : online at https://bigbluebutton.math.upmc.fr/b/ade-phf-9dg

Sujet : Pathwise Regularisation of McKean--Vlasov Equations

Résumé :
Abstract: McKean—Vlasov equations and mean field approximations are a well established modelling tool and area of important mathematical study. A challenging and still unsolved problem is to obtain rigorous results concerning the validity of such approximations to many particle systems, especially when the interaction is singular in some sense.

In this talk I will present a work in preparation by myself and F. Harang (University of Oslo) where we consider a certain random perturbation of such singular kernels that yields well-posedness of the mean field equation and rigorous mean field limit results for the particle system. Our approach uses recent ideas from Cattier & Gubinelli ’16 (https://arxiv.org/pdf/1205.1735.pdf), Harang & Perkowski ’20 (https://arxiv.org/pdf/2003.05816.pdf) and Galeati & Gubinelli ’20 (https://arxiv.org/pdf/2004.00872.pdf) to obtain a path-wise regularisation of such equations, combined with the pathwsie approach to classical McKean-Vlasov equations presented by Friz et al ’19 (https://arxiv.org/pdf/1812.11773.pdf).

In the talk I will firstly, give a brief introduction to the theory of McKean-Vlasov/mean field problems in general as well as the path-wise regularisation results mentioned above. Then I will explain our new result for regularised particle systems.