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SUMMARY:Pathwise Regularisation of McKean-Vlasov problems - Avi Mayorcas (
 University of Oxford)
DTSTART:20200515T110000Z
DTEND:20200515T120000Z
UID:TALK142327@talks.cam.ac.uk
CONTACT:Renato Velozo
DESCRIPTION:McKean—Vlasov equations are a well established modelling too
 l and area of important mathematical study. A challenging and still unsolv
 ed problem is to obtain rigorous results concerning the validity of mean-f
 ield approximations to such systems\, especially when the interaction is s
 ingular.\n\nIn this talk I will present a work in preparation by myself an
 d F. Harang (University of Oslo) where we consider a random perturbation o
 f such singular kernels that yields well-posedness of the mean field equat
 ion and rigorous mean field limit results for the particle system. The app
 roach is based on the notion of a local-time and encapsulates the physical
  intuition that at small scales it is extremely unlikely for two particles
  to be in exactly the same location.\n\nOur approach uses recent ideas fro
 m Cattier & Gubinelli ’16 (https://arxiv.org/pdf/1205.1735.pdf)\, Harang
  & Perkowski ’20 (https://arxiv.org/pdf/2003.05816.pdf) and Galeati & Gu
 binelli ’20 (https://arxiv.org/pdf/2003.05816.pdf) to obtain a path-wise
  regularisation of such equations\, combined with the path-wise approach t
 o classical McKean-Vlasov equations presented by Friz et al ’19 (https:/
 /arxiv.org/pdf/1812.11773.pdf).\n\nIn the talk I will firstly\, give a bri
 ef introduction to the theory of McKean-Vlasov/mean field problems in gene
 ral as well as the path-wise regularisation results mentioned above. Then 
 I will explain our new result for regularised particle systems. 
LOCATION:Online (Ask for the link to rav25@cam.ac.uk)
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