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Cumulants on the Wiener space |
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| Authors: | Ivan Nourdin |
| Affiliation: | a Laboratoire de Probabilités et Modèles Aléatoires, Université Paris VI, Boîte courrier 188, 4 Place Jussieu, 75252 Paris Cedex 5, France b Equipe Modal'X, Université Paris Ouest - Nanterre la Défense, 200 Avenue de la République, 92000 Nanterre, France c LSTA, Université Paris VI, France |
| 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. |
| Keywords: | Cumulants Diagram formulae Gaussian processes Malliavin calculus Ornstein-Uhlenbeck semigroup |
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