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arXiv · 0910.1996

Cumulants on the Wiener Space

Ivan Nourdin·Giovanni Peccati
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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.

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Ivan Nourdin, Giovanni Peccati. 2009-10-12. Cumulants on the Wiener Space. https://arxiv.org/abs/0910.1996

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