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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, butfatcat:o5yh2y6b7jdgblwelbkw4s34ui