Ivan Nourdin, Giovanni Peccati
Published 2009-10-12Version 1
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.
Second order Poincaré inequalities and CLTs on Wiener space
Entropy, Invertibility and Variational Calculus of the Adapted Shifts on Wiener space
On fractional smoothness and $L_p$-approximation on the Gaussian space
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