An Optimal Functional It\^{o}'s Formula For L\'{e}vy Processes

TL;DR

This paper introduces a new local time-space Itô's formula for Lévy processes that applies to bounded, continuous functionals without requiring Hölder continuity, advancing the functional stochastic calculus.

Contribution

It provides a novel local time-space Itô's formula for Lévy processes applicable to all bounded, continuous functionals, independent of Hölder conditions.

Findings

New local time-space Itô's formula for Lévy processes

Applicable to arbitrary bounded, continuous functionals

Does not depend on Hölder continuity

Abstract

Several versions of It\^{o}'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 L\'{e}vy processes and which does not depend on a functional's H\"{o}lder continuity.