Français
Rearranged stochastic heat equation
Multi angle
Authors : Delarue, François (Author of the conference)
CIRM (Publisher )
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
Additional resources :
https://www.cirm-math.fr/RepOrga/2390/Slides/Francois_Delarue.pdf
CIRM (Publisher )
Loading the player...
|
Abstract :
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).
MSC Codes : 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
Additional resources :
https://www.cirm-math.fr/RepOrga/2390/Slides/Francois_Delarue.pdf
|
Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 27/09/2023 Conference Date : 07/09/2023 Subseries : Research talks arXiv category : Probability Mathematical Area(s) : Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:42:27 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-09-07_Delarue_compo.mp4 
|
Information on the Event
Event Title : A Random Walk in the Land of Stochastic Analysis and Numerical Probability / Une marche aléatoire dans l'analyse stochastique et les probabilités numériquesEvent Organizers : Champagnat, Nicolas ; Pagès, Gilles ; Tanré, Etienne ; Tomašević, Milica Dates : 04/09/2023 - 08/09/2023 Event Year : 2023 Event URL : https://conferences.cirm-math.fr/2390.html
Citation Data
DOI : 10.24350/CIRM.V.20088803Cite this video as: 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 |
See Also
- [Multi angle] Two examples of thermodynamic limits in neuroscience / Author of the conference Faugeras, Olivier.
- [Multi angle] Conditional propagation of chaos for generalized Hawkes processes having alpha-stable jump heights / Author of the conference Löcherbach, Eva.
- [Multi angle] Recent results on epidemic models / Author of the conference Pardoux, Etienne.
- [Multi angle] Functional convex order for stochastic processes: a constructive (and simulable) approach / Author of the conference Pagès, Gilles.
- [Multi angle] Optimal revelated utilities and convex pricing kernels: - a forward point of view of convexity propagation / Author of the conference El Karoui, Nicole.
- [Multi angle] Stochastic control for medical treatment optimization / Author of the conference de Saporta, Benoîte.
- [Multi angle] Systematic jump risk / Author of the conference Jacod, Jean.
- [Multi angle] Propagation of chaos for stochastic particle systems with singular mean-field interaction of $L^{q}-L^{p}$ type / Author of the conference Tomašević, Milica.
- [Multi angle] Construction of Boltzmann and McKean Vlasov type flows (the sewing lemma approach) / Author of the conference Bally, Vlad.
- [Multi angle] Wasserstein convergence of penalized Markov processes / Author of the conference Champagnat, Nicolas.
- [Multi angle] Exponent dynamics for branching processes / Author of the conference Méléard, Sylvie.
- [Multi angle] Gambling for resurrection and the heat equation on a triangle / Author of the conference Blanchet-Scalliet, Christophette.
- [Multi angle] Cox Construction: a random walk in the land of stochastic analysis and numerical probability / Author of the conference Protter, Philip.
- [Multi angle] Large random matrices and PDE's / Author of the conference Lions, Pierre-Louis.
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
Imagette Video
