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Date: 9 Jul. (Thu.)
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Place: On the Web
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Time: 16:30-18:00
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Speaker: Noufel Frikha (Université de Paris)
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Title: Well-posedness of McKean-Vlasov SDEs, related PDE on the Wasserstein space and some new quantitative estimates for propagation of chaos.
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Abstract:
In this talk, i will present some new well-posedness results for non-linear diffusion/jump processes in the sense of McKean-Vlasov which go beyond the (well-understood) Cauchy-Lipschitz theory (see e.g. the course at St-Flou of A.S. Sznitman). For non-linear diffusion processes, I will show how the underlying noise regularizes the system and allows to establish the existence and the regularity properties of the transition density with respect to the measure argument, under a uniform ellipticity assumption. I will present the link between this smoothing effect with respect to the initial measure and the Backward Kolmogorov PDE on the Wasserstein space, which is the space of probability measures with finite second order moment. Finally, I will show how classical solutions to this PDE play a key role to establish some new quantitative estimates of propagation of chaos for the approximation of the mean-field dynamics by the related particle system.
This presentation is based on some recent works in collaboration with: P.-E. Chaudru de Raynal (Université Savoie Mont Blanc), V. Konakov (HSE Moscou), L. Li (UNSW Sydney) and S. Menozzi (Université d’Evry Val d’Essone).
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