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CATEGORIES:Cambridge Analysts' Knowledge Exchange
SUMMARY:Pathwise Regularisation of McKean-Vlasov problems
- Avi Mayorcas (University of Oxford)
DTSTART;TZID=Europe/London:20200515T120000
DTEND;TZID=Europe/London:20200515T130000
UID:TALK142327AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/142327
DESCRIPTION:McKean—Vlasov equations are a well established mod
elling tool and area of important mathematical stu
dy. A challenging and still unsolved problem is to
obtain rigorous results concerning the validity o
f mean-field approximations to such systems\, espe
cially when the interaction is singular.\n\nIn thi
s talk I will present a work in preparation by mys
elf and F. Harang (University of Oslo) where we co
nsider a random perturbation of such singular kern
els that yields well-posedness of the mean field e
quation and rigorous mean field limit results for
the particle system. The approach is based on the
notion of a local-time and encapsulates the physic
al intuition that at small scales it is extremely
unlikely for two particles to be in exactly the sa
me location.\n\nOur approach uses recent ideas fro
m Cattier & Gubinelli ’16 (https://arxiv.org/pdf/1
205.1735.pdf)\, Harang & Perkowski ’20 (https://ar
xiv.org/pdf/2003.05816.pdf) and Galeati & Gubinell
i ’20 (https://arxiv.org/pdf/2003.05816.pdf) to ob
tain a path-wise regularisation of such equations\
, combined with the path-wise approach to classica
l 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 brief introductio
n to the theory of McKean-Vlasov/mean field proble
ms in general as well as the path-wise regularisat
ion results mentioned above. Then I will explain o
ur new result for regularised particle systems.
LOCATION:Online (Ask for the link to rav25@cam.ac.uk)
CONTACT:Renato Velozo
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