Canonical L´ evy process and Malliavin calculus I

A suitable canonical Lprocess is constructed in order to study a Malliavin calculus based on a chaotic representation property of Lprocesses proved by Itˆ o using multiple two-parameter integrals. In this setup, the two-parameter derivative Dt,x is studied, depending on whether x = 0 or x 6= 0; in the first case, we prove a chain rule; in the second case, a formula by trajectories. c 2006 Elsevier B.V. All rights reserved.