# 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)
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.