Functions of Bounded Variation on the Classical Wiener Space and an Extended Ocone-Karatzas Formula

Maurizio Pratelli, Dario Trevisan

Published 2011-09-23, updated 2011-10-02Version 2

We prove an extension of the Ocone-Karatzas integral representation, valid for all $BV$ functions on the classical Wiener space. We establish also an elementary chain rule formula and combine the two results to compute explicit integral representations for some classes of $BV$ composite random variables.