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Cumulants on the Wiener space

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jun 2010Embargo end date: 01 Jan 2009 France, France, France, Luxembourg English Publisher:Elsevier BVJournal:Journal of Functional Analysis, volume 258, pages 3,775-3,791 (issn: 0022-1236, Copyright policy )
Authors: Nourdin, Ivan; Peccati, Giovanni;

doi: 10.1016/j.jfa.2009.10.024 , 10.48550/arxiv.0910.1996

arXiv: 0910.1996

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.

18 pages

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France, France, France, Luxembourg
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Keywords

Ornstein–Uhlenbeck semigroup, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Stochastic calculus of variations and the Malliavin calculus, Malliavin calculus, Gaussian processes, Ornstein-Uhlenbeck semigroup, 60H07, 60H05, 60F05, FOS: Mathematics, Mathematics - Combinatorics, 60F05; 60G15; 60H05; 60H07, Gaussian Processes, Diagram formulae, Diagram Formulae, Cumulants, Probability (math.PR), [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], Ornstein-Uhlenbeck Semigroup, cumulants, 60G15, : Mathematics [G03] [Physical, chemical, mathematical & earth Sciences], : Mathématiques [G03] [Physique, chimie, mathématiques & sciences de la terre], Combinatorics (math.CO), Analysis, Mathematics - Probability

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
44
Top 10%
Top 10%
Top 10%
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