Cumulants on the Wiener Space

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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Journal of Functional Analysis, Elsevier, 2010
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  • HAL Id : hal-00423831, version 1
  • ARXIV : 0910.1996

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Ivan Nourdin, Giovanni Peccati. Cumulants on the Wiener Space. Journal of Functional Analysis, Elsevier, 2010. 〈hal-00423831〉

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