Canonical Lévy process and Malliavin calculus

A suitable canonical Lévy process is constructed in order to study a Malliavin calculus based on a chaotic representation property of Lévy processes proved by Itô using multiple two-parameter integrals. In this setup, the two-parameter derivative D t , x is studied, depending on whether x = 0 or x ≠ 0 ; in the first case, we prove a chain rule; in the second case, a formula by trajectories.