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arXiv · 2112.14221

On the Functional L\'{e}vy-It\^{o} Stochastic Calculus

Christian Houdré·Jorge Víquez
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Abstract

Several versions of It\^{o}'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 It\^{o}'s formula and corresponding calculus. Second, for L\'{e}vy processes, an optimal local-time based It\^{o}'s formula is obtained. Some quick applications are then given.

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BibTeXRIS

Christian Houdré, Jorge Víquez. 2021-12-28. On the Functional L\'{e}vy-It\^{o} Stochastic Calculus. https://arxiv.org/abs/2112.14221

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