Functions of bounded variation on the classical Wiener space and an extended Ocone-Karatzas formula (Q429294)

The aim of this article is to slightly extend the Clark-Ocone (or Ocone-Karatzas) formula, very classical in Malliavin calculus, to functions which need not be smooth in the Malliavin sense (more precisely, in \(\mathbb{D}^{1,1}\)). Thus the authors consider so-called ``functions of bounded variation'' on the Wiener space, namely those functions \(f\) that admit an \(L^2[0,T)\)-valued measure, still denoted by \(Df\), such that the formal integration by parts formula still holds. Such functions are also characterized as the \(L^1\)-limits of sequences which are bounded in \(\mathbb{D}^{1,1}\).NEWLINENEWLINE After the proof of the extended Clark-Ocone-Karatzas formula, the authors provide a chain rule formula and two examples of explicit representation of the density of \(Df\).