On the Functional Lévy-Itô Stochastic Calculus

Christian Houdré; Jorge Víquez

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arXiv · 2112.14221

On the Functional Lévy-Itô Stochastic Calculus

Christian Houdré·Jorge Víquez

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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.

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Christian Houdré, Jorge Víquez. 2022-02-24. On the Functional Lévy-Itô Stochastic Calculus. https://arxiv.org/abs/2112.14221

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