A Girsanov result for the Pettis integral

TL;DR

This paper presents a Pettis integral representation for Banach-valued Itô processes and demonstrates how to modify their drift terms using a Girsanov Theorem, extending stochastic calculus tools.

Contribution

It introduces a Girsanov theorem for Pettis integrals in Banach spaces, enabling drift modifications of Banach-valued Itô processes.

Findings

Pettis integral representation for Banach-valued Itô processes

Girsanov theorem applied to Pettis integrals

Drift term modification in Banach space stochastic processes

Abstract

A kind of Pettis integral representation for a Banach valued It\^o process is given and its drift term is modified using a Girsanov Theorem.