Averaging and homogenization in deterministic and stochastic systems / Moyennisation et homogénéisation dans les systèmes déterministes et stochastiques

Collection Averaging and homogenization in deterministic and stochastic systems / Moyennisation et homogénéisation dans les systèmes déterministes et stochastiques

Organisateur(s) Liverani, Carlangelo ; Melbourne, Ian ; Pavliotis, Grigorios ; Olla, Stefano

Date(s) 11/05/2015 - 15/05/2015

URL associée http://conferences.cirm-math.fr/1198.html

3 5

Chapitres

Pathwise regularisation by noise in PDEs

De Massimiliano Gubinelli

We discuss some examples of the "good" effects of "very bad", "irregular" functions. In particular we will look at non-linear differential (partial or ordinary) equations perturbed by noise. By defining a suitable notion of "irregular" noise we are able to show, in a quantitative way, that the more the noise is irregular the more the properties of the equation are better. Some examples includes: ODE perturbed by additive noise, linear stochastic transport equations and non-linear modulated dispersive PDEs. It is possible to show that the sample paths of Brownian motion or fractional Brownian motion and related processes have almost surely this kind of irregularity. (joint work with R. Catellier and K. Chouk)

Informations sur la vidéo

Date de captation 13/05/2015
Date de publication 28/05/2015
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.18762503
Citer cette vidéo Gubinelli, Massimiliano (13/05/2015). Pathwise regularisation by noise in PDEs. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18762503
URL https://dx.doi.org/10.24350/CIRM.V.18762503

Domaine(s)

Bibliographie

Beck, L., Flandoli, F., Gubinelli, M., & Maurelli, M. (2014). Stochastic ODEs and stochastic linear PDEs with critical drift: regularity, duality and uniqueness. <arXiv:1401.1530> - http://arxiv.org/abs/1401.1530
Catellier, R. (2015). Rough linear transport equation with an irregular drift. <arXiv:1501.03000> - http://arxiv.org/abs/1501.03000
Catellier, R., & Gubinelli, M. (2014). Averaging along irregular curves and regularisation of ODEs. <arXiv:1205.1735> - http://arxiv.org/abs/1205.1735
Chouk, K., & Gubinelli, M. (2015). Nonlinear PDEs with modulated dispersion I: Nonlinear Schrödinger equations. <arXiv:1303.0822> - http://arxiv.org/abs/1303.0822
Chouk, K., & Gubinelli, M. (2014). Nonlinear PDEs with modulated dispersion II: Korteweg--de Vries equation. <arXiv:1406.7675> - http://arxiv.org/abs/1406.7675