Dear Colleagues,

We would like to invite you to the following Probability seminar that will take place on June 26, 2020 at 11 by the zoom platform.

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Speaker: Lucio Galeati (University of Bonn) Title: Regularisation by noise and notions of irregularity

June 26, 2020 (Friday) - 11:00 - zoom link: TBA

The link and password to access the seminar will be available at the following webpage https://www.math.unipd.it/~bianchi/seminari/

Abstract: A natural question in the field of regularisation by noise phenomena is to understand under which conditions on a path $w$, the additively perturbed ODE $x'=b(x)+w'$ is well-posed, even when its unperturbed counterpart $x'=b(x)$ is not. In order to answer this question, Catellier and Gubinelli (SPA 2016) introduced the theory of nonlinear Young integrals and the concept of $\rho$-irregularity of $w$; they also proved that fBm paths are $\rho$-irregular. In this talk, I will first review their work and then present its more recent extensions. The property of $\rho$-irregularity can be linked to the regularity of the local time of $w$ and, in the case of Gaussian processes, can be established under a suitable local non-determinism (LND) condition. Moreover, it can be shown that $\rho$-irregular paths are necessarily nowhere $\alpha$-Holder continuous, for suitable values $\alpha=\alpha(\rho)$. This gives a rigorous proof of the frequently observed paradigm "the rougher the noise, the better the regularisation". Based on joint works with Massiliano Gubinelli.

--------------- David Barbato Dip. di Matematica Università di Padova

Via Trieste, 63 - 35121 Padova, Italy