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

TL;DR

This paper extends the Ocone-Karatzas integral representation to all BV functions on the classical Wiener space, providing new formulas and explicit representations for composite random variables.

Contribution

It introduces an extended Ocone-Karatzas formula for BV functions and derives an elementary chain rule on Wiener space, enabling explicit integral representations.

Findings

Extended Ocone-Karatzas formula valid for all BV functions

Elementary chain rule for BV functions on Wiener space

Explicit integral representations for certain BV composite variables

Abstract

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.