Pathwise calculus for non-anticipative functionals

Abstract

The focus of these lectures is to define a calculus which can be used to describe the variations of interesting classes of functionals of a given reference stochastic process X. In order to cover interesting examples of processes, we allow X to have right-continuous paths with left limits, i.e., its paths lie in the space $D\left( {\left[ {0,\,T} \right],\,{\mathbb{R}}^d } \right)$ of càdlàg paths.