Cumulants on the Wiener space

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 fixedWiener chaos, virtually replacing the usual “graph/diagram computations” adopted in most of the probabilistic literature. © 2009 Elsevier Inc. All rights reserved