Stochastic integration in Banach spaces - a survey

TL;DR

This survey reviews stochastic integration in Banach spaces, focusing on martingale type 2 and UMD spaces, and discusses applications like Malliavin calculus and stochastic maximal regularity, including a new proof of the latter.

Contribution

It provides a comprehensive overview of stochastic integration in Banach spaces and introduces a new proof for stochastic maximal regularity.

Findings

Exposition of stochastic integrals in martingale type 2 and UMD spaces

Applications to vector-valued Malliavin calculus

A new proof of the stochastic maximal regularity theorem

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.