An anticipating Itô formula for Lévy processes release_o5yh2y6b7jdgblwelbkw4s34ui

by Elisa Alós, Jorge León, Josep Vives

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2008  

Abstract

In this paper, we use the Malliavin calculus techniques to obtain an anticipative version of the change of variable formula for Lévy processes. Here the coefficients are in the domain of the anihilation (gradient) operator in the "future sense", which includes the family of all adapted and square-integrable processes. This domain was introduced on the Wiener space byAì os and Nualart (1998). Therefore, our Itô formula is not only an extension of the usual adapted formula for Lévy processes, but also an extension of the anticipative version on Wiener space obtained inAì os and Nualart (1998).
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