English
Rearranged stochastic heat equation
Multi angle
Auteurs : Delarue, François (Auteur de la conférence)
CIRM (Editeur )
47D07 - Markov semigroups of linear operators and applications to diffusion processes
60G57 - Random measures
60H15 - Stochastic partial differential equations
60J35 - Transition functions, generators and resolvents
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2390/Slides/Francois_Delarue.pdf
CIRM (Editeur )
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Résumé :
We provide an explicit construction of a strong Feller semigroup on the space of 1d probability measures that maps bounded measurable functions into Lipschitz continuous functions, with a Lipschitz constant that blows up in an integrable manner in small time. The construction relies on a rearranged version of the stochastic heat equation on the circle driven by a coloured noise. Under the action of the rearrangement, the solution is forced to live in a space of quantile functions that is isometric to the space of probability measures on the real line. As an application, we show that the noise resulting from this approach can be used to perturb, in an ergodic manner, gradient flows on the space of 1d probability measures. We also show that the same noise can be used to enforce uniqueness to some types of mean field games.
Based on joint works with William Hammersley (Nice) and Youssef Ouknine (Marrakech).
Codes MSC : Based on joint works with William Hammersley (Nice) and Youssef Ouknine (Marrakech).
47D07 - Markov semigroups of linear operators and applications to diffusion processes
60G57 - Random measures
60H15 - Stochastic partial differential equations
60J35 - Transition functions, generators and resolvents
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2390/Slides/Francois_Delarue.pdf
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de Publication : 27/09/2023 Date de Captation : 07/09/2023 Sous Collection : Research talks Catégorie arXiv : Probability Domaine(s) : Probabilités & Statistiques Format : MP4 (.mp4) - HD Durée : 00:42:27 Audience : Chercheurs ; Etudiants Science Cycle 2 ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-09-07_Delarue_compo.mp4 
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Informations sur la Rencontre
Nom de la Rencontre : A Random Walk in the Land of Stochastic Analysis and Numerical Probability / Une marche aléatoire dans l'analyse stochastique et les probabilités numériquesOrganisateurs de la Rencontre : Champagnat, Nicolas ; Pagès, Gilles ; Tanré, Etienne ; Tomašević, Milica Dates : 04/09/2023 - 08/09/2023 Année de la rencontre : 2023 URL de la Rencontre : https://conferences.cirm-math.fr/2390.html
Données de citation
DOI : 10.24350/CIRM.V.20088803Citer cette vidéo: Delarue, François (2023). Rearranged stochastic heat equation. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20088803 URI : http://dx.doi.org/10.24350/CIRM.V.20088803 |
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Bibliographie
- DELARUE, François et HAMMERSLEY, William RP. Rearranged Stochastic Heat Equation. arXiv preprint arXiv:2210.01239, 2022. - https://doi.org/10.48550/arXiv.2210.01239
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