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SUMMARY:McKean-Vlasov SDEs\, related PDEs on the Wasserstein space\, and a
 pplications
DTSTART:20260526T070000Z
DTEND:20260526T084500Z
DTSTAMP:20260607T043100Z
UID:indico-event-14483@indico.math.cnrs.fr
DESCRIPTION:Speakers: Noufel Frikha (Université Panthéon Sorbonne)\n\nWe
  will explore recent advances concerning nonlinear diffusion processes in 
 the sense of McKean-Vlasov\, and their connections to partial differential
  equations (PDEs) defined on the Wasserstein space\, that is\, the space o
 f probability measures with finite second order moment. We will discuss re
 cent results on the well-posedness - both in the weak and strong sense - o
 f such dynamics driven by Brownian motion and/or jump processes\, beyond t
 he classical Cauchy-Lipschitz framework.In the Brownian setting\, I will d
 iscuss the regularization effect of the noise\, notably the existence and 
 smoothness of the transition density - particularly in the measure argumen
 t - under uniform ellipticity assumptions. These smoothing effects are cru
 cial for establishing the existence and uniqueness of solutions to the Kol
 mogorov-type PDEs posed on the Wasserstein space.Such infinite-dimensional
  PDEs play a central role in deriving quantitative propagation of chaos es
 timates for mean-field approximations via interacting particle systems. Fi
 nally\, if time permits\, I will discuss the numerical approximation of th
 ese equations using the Euler-Maruyama time discretization scheme at the l
 evel of the particle system.\n\nhttps://indico.math.cnrs.fr/event/14483/
LOCATION: Amphi Schwartz
URL:https://indico.math.cnrs.fr/event/14483/
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