Commutation of variation and dual projection

Abstract

For a raw process of integrable variation V, taking values in a Banach space E having the Radon-Nikodyn property, the variation of the predictable (optional) dual projection is the predictable (optional) dual projection of the variation. An analogous result holds for the associated stochastic measures. The result is applied to the stochastic integral of a real, optional process H with respect to V when V is adapted.