arXiv subjects
Publications and source records attributed to Jorge Víquez.
Motivated by extending the functional stochastic calculus, to important functionals to which it does not apply, a notion of functional derivative along a curve is introduced. This new setting is developed by incorporating path-dependent directional extensions. Our results then focus on a comprehensive exploration of these derivatives and the insights they provide on the structure of functionals.
Several versions of Itô's formula have been obtained in the setting of the functional stochastic calculus. In this regard, we present a local time-space version that works for arbitrary bounded and continuous functionals of Lévy processes and which does not depend on a functional's Hölder continuity.
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.