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Inégalités de Sobolev logarithmiques pour des problèmes d'évolution non linéaires

Abstract : We study nonlinear partial differential equations of McKean-Vlasov type. We establish logarithmic Sobolev inequalities for the associated particle systems in mean field interaction. With an additionnal propagation of chaos result, we show that it is possible to recover the long time behaviour of the nonlinear equation from the one of the particle system. At last, we provide exact confidence intervals for the convergence of Monte-Carlo method for both explicit and implicit Euler schemes associated to a diffusion process. In particular, these results can be employed for the McKean-Vlasov equations.
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https://tel.archives-ouvertes.fr/tel-00001287
Contributor : Florent Malrieu <>
Submitted on : Wednesday, March 27, 2002 - 5:49:54 PM
Last modification on : Friday, January 10, 2020 - 9:08:06 PM
Long-term archiving on: : Friday, April 2, 2010 - 7:53:46 PM

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  • HAL Id : tel-00001287, version 1

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Florent Malrieu. Inégalités de Sobolev logarithmiques pour des problèmes d'évolution non linéaires. Mathématiques [math]. Université Paul Sabatier - Toulouse III, 2001. Français. ⟨tel-00001287⟩

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