Stochastic integration in Banach spaces - a survey

Abstract

This paper presents a brief survey of the theory of stochastic integration in Banach spaces. Expositions of the stochastic integrals in martingale type 2 spaces and UMD spaces are presented, as well as some applications of the latter to vector-valued Malliavin calculus and the stochastic maximal regularity problem. A new proof of the stochastic maximal regularity theorem is included.

minor corrections. To appear in the proceedings of the 2012 EPFL Semester on Stochastic Analysis and Applications