On the Functional Levy-Ito Stochastic Calculus
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.
On the Functional Lévy-Itô Stochastic Calculus Christian Houdré∗ and Jorge Vı́quez† February 25, 2022 arXiv:2112.14221v2 [math.PR] 24 Feb 2022 Abstract Several versions of Itô’s formula have been obtained in the context of the functional stochastic…
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