Mathematisches Kolloquium

The next talk in the mathematical colloquium will take place Friday, 23 April 2021, 2:15 pm via zoom.

Title: Gradient estimates on the Lévy-Itô space, Hölder spaces, and Riemann-Liouville operators
Speaker: Prof. Dr. Stefan Geiss (University of Jyväskylä) hosted by Prof. Dr. Bender
In a stochastic framework we consider the interplay between Riemann-Liouville operators applied to right-continuous stochastic processes with left limits, real interpolation,and bounded mean oscillation.
We discuss some of these connections for Hilbert space valued gradient processes on the Lévy-Itô space appearing from non-local partial integrodierential equations with a Hölder terminal condition. We prove upper and lower bounds for these gradients that depend on the direction in which the gradient is inspected. The quantitative behavior of these directional gradients is needed for applications of Galtchouck-Kunita-Watanabe projections.
This is joint work with Thuan Nguyen (Saarland University).