# 19 mars 2019: 1 événement

### Mardi 19 mars 13:45-15:00 - Emiel Lorist - Delft

Singular stochastic integral operators

Résumé : Singular stochastic integrals of the form
$$S_K G(t) :=\int_0^\infty K(t,s) G(s) \,\mathrmd W_H(s), \qquad t\in \mathbbR_+,$$
appear naturally in questions related to stochastic maximal regularity. Here $G$ is an adapted process, $W_H$ is a cylindrical Brownian motion and $K$ is allowed be singular.
In this talk I will introduce Calder\’on—Zygmund theory for such singular stochastic integrals with operator-valued kernel $K$.
I will first discuss $L^p$-extrapolation under a H\"ormander condition on the kernel. Afterwards I will treat sparse domination and sharp weighted bounds under a Dini condition on the kernel, leading to a stochastic analog of the solution to the $A_2$-conjecture.
The developed theory implies $p$-independence and weighted bounds for stochastic maximal $L^p$-regularity both in the complex and real interpolation scale. This leads to mixed $L^p(L^q)$-theory for several stochastic partial differential equations, of which I will give a few examples.
This talk is based on joint work with Mark Veraar.

En savoir plus : Séminaire d’Analyse Fonctionnelle

# 19 mars 2019: 1 événement

### Mardi 19 mars 11:00-12:30 - Debora Amadori - Université de l'Aquila

Séminaires Equations aux Dérivées Partielles

Résumé : GdT CLAWS : Groupe de travail autour des lois de conservation

Lieu : 324-2B

En savoir plus : Séminaires Equations aux Dérivées Partielles