Zusammenfassung für den Vortrag am 05.06.2020 (11:00 Uhr)

Arbeitsgemeinschaft ANGEWANDTE ANALYSIS

Lucio Galeati (Universität Bonn)
An analytic approach to regularization by noise phenomena for ODEs

One of the main questions in regularisation by noise literature is

to understand whether an additive perturbation restores well-posedness of an

ODE, i.e. under which conditions there exists a unique solution to

$\dot{x}=b(x)+\dot{w}$ even if this is not the case for $w=0$.

Davie first addressed the problem of identifying the analytical properties

of a path $w$ which provide a regularising effect; Catellier and Gubinelli

answered the problem by introducing the key concepts of averaging operators

and nonlinear Young integrals.

Remarkably, this allows to provide a consistent solution theory even when

$b$ is merely distributional and to deduce that generic continuous

functions have an arbitrarily high regularisation effect.

In this talk I will first review their work and then present its more recent

extensions. Based on a joint work with Massimiliano Gubinelli.

One day before the seminar, an announcement with the link will be sent to the mailing list of the AG seminar. If you are not on the mailing list, but still want to join the broadcast, please contact Pavlos Tsatsoulis.


07.06.2020, 02:30