# 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 articles
Journal of Functional Analysis, Elsevier, 2010
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https://hal.archives-ouvertes.fr/hal-00423831
Contributor : Ivan Nourdin <>
Submitted on : Monday, October 12, 2009 - 7:40:29 PM
Last modification on : Thursday, March 16, 2017 - 1:07:44 AM
Document(s) archivé(s) le : Wednesday, June 16, 2010 - 12:41:15 AM

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### Identifiers

• HAL Id : hal-00423831, version 1
• ARXIV : 0910.1996

### Citation

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

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