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 Dt,x is studied, depending on whether x=0 or...

Let M be a continuous two-parameter L4-martingale, vanishing on the axes, and f a 1-function. In Itô's formula for f(M2) a new martingale M is involved. This martingale can be interpreted formally as the stochastic integral [integral operator][not partial differential]1M[not partial...