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1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires 2 MODAL-X - Modélisation aléatoire de Paris X

Abstract : We combine infinite-dimensional integration by parts procedures with a recursive relation on moments reminiscent of a formula by Barbour 1986, and deduce explicit expressions for cumulants of functionals of a general Gaussian field. These findings yield a compact formula for cumulants on a fixed Wiener chaos, virtually replacing the usual ``graph-diagram computations- adopted in most of the probabilistic literature.

keyword : Ornstein-Uhlenbeck Semigroup Malliavin calculus Gaussian Processes Cumulants Diagram Formulae

Author: Ivan Nourdin - Giovanni Peccati -



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