Rearranged stochastic heat equation | Vidéo | Carmin.tv

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Rearranged stochastic heat equation

By François Delarue

Appears in collection : A Random Walk in the Land of Stochastic Analysis and Numerical Probability / Une marche aléatoire dans l'analyse stochastique et les probabilités numériques

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).

Information about the video

Date of recording 07/09/2023
Date of publication 27/09/2023
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.20088803
Cite this video DELARUE, François (07/09/2023). Rearranged stochastic heat equation. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20088803
URL https://dx.doi.org/10.24350/CIRM.V.20088803

Domain(s)

Probability

Bibliography

DELARUE, François et HAMMERSLEY, William RP. Rearranged Stochastic Heat Equation. arXiv preprint arXiv:2210.01239, 2022. - https://doi.org/10.48550/arXiv.2210.01239

MSC codes

Document(s)

https://www.cirm-math.fr/RepOrga/2390/Slides/Francois_Delarue.pdf

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