Seminario de Análisis 

Fecha y hora: 26 de Abril, 11:30-12:30

Lugar: Aula 520, Módulo 17, UAM

Ponente: Jan van Neerven

Título: Stochastic integration in UMD Banach spaces, an overview
Abstract: The class of UMD Banach spaces is of central importance in vector-valued harmonic analysis and stochastic analysis. In this overview talk, we outline the theory of stochastic integration developed over the past two decades in collaboration with Mark Veraar and Lutz Weis. In this theory, a decoupling method is used to replace the classical Ito isometry by a two-sided estimate involving Gaussian sums. In the case where the Banach space is an L^p-space, it reduces to a two-sided square function estimate. This result has led to the solution of the so-called stochastic maximal regularity problem. This, in turn, has opened the way to many interesting applications in nonlinear stochastic PDEs.