An averaging (path-by-path) approach to regularisation by noise for ODEs

schedule le lundi 01 juin 2020 de 17h00 à 18h00

Organisé par : F. Bechtold, W. Da Silva , A. Fermanian, S. Has, Y. Yu

Intervenant : Lucio Galeati (Universität Bonn)
Lieu : online at https://bigbluebutton.math.upmc.fr/b/ade-phf-9dg

Sujet : An averaging (path-by-path) approach to regularisation by noise for ODEs

Résumé :

ABSTRACT: One of the main questions in regularisation by noise phenomena is to understand under which conditions the introduction of an additive perturbation $w$ (usually sampled as a stochastic process, e.g. Brownian motion) allows to restore wellposedness of a given ODE $\dot{x}=b(x)$.

Davie first addressed the following more subtle questions: what are the analytical properties of a path $w$ which provide a regularizing effect? Which classes of stochastic processes satisfy these properties?

Catellier and Gubinelli answered them by introducing the key concepts of averaging operators and nonlinear Young integrals; this allows to consider $w$ sampled as an fBm and to provide a consistent solution theory even when $b$ is merely distributional.

In this talk I will first review their work and then present its more recent extensions. Based on a joint work with Massimiliano Gubinelli.