Canonical Lévy process and Malliavin calculus

A suitable canonical Levy process is constructed in order to study a Malliavin calculus based on a chaotic representation property of Levy processes proved by Ito using multiple two-parameter integrals. In this setup, the two-parameter derivative Dt,x is studied, depending on whether x=0 or x[not equal to]0; in the first case, we prove a chain rule; in the second case, a formula by trajectories.