An optimal Itô formula for Lévy processes
Résumé
Several Ito formulas have been already established for Levy processes. We explain according to which criteria they are not optimal and establish an extended Ito formula that satisfies that criteria. The interest, in particular, of this formula, is to obtain the explicit decomposition of F(X(t), t), for X Levy process and F deterministic function with locally bounded first order Radon-Nikodym derivatives, as the sum of a Dirichlet process and a bounded variation process.