Representation of the distributions on Wiener space and stochastic calculus of variations

Abstract

In this work we construct projections and dual projections with respect to the past of the Wiener process for the Cameron-Martin space-valued distributions on the Wiener space. With their help we then prove, on the one hand, an extension of Clark's formula to the representation of the scalar distributions with the extended Itô integral and, on the other hand, we give a decomposition of the vector-valued distributions by exactly calculating the kernel of the divergence operator.