On the Functional Lévy-Itô Stochastic Calculus

Abstract

Several versions of Itô's formula have been obtained in the context of the functional stochastic calculus. Here, we revisit this topic in two ways. First, by defining a notion of derivative along a functional, we extend the setting of the (semimartingale) functional Itô's formula and corresponding calculus. Second, for Lévy processes, an optimal local-time based Itô's formula is obtained. Some quick applications are then given.

The second version included remark 4.6(iv), improved wording, fixed typos, and included more references