Laboratoire de Mathématiques de Besançon - UMR 6623 CNRS

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19 mars 2019: 1 événement

  • Séminaire d’Analyse Fonctionnelle

    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