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Yet another proof of the Nualart-Peccati criterion

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Yet another proof of the Nualart-Peccati criterion
2.	Creator	Author's name, affiliation, country	Ivan Nourdin; Université Nancy 1
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Brownian motion; free Brownian motion; multiple Wiener-Itô integrals; multiple Wigner integrals; Nualart-Peccati criterion; product formula
3.	Subject	Subject classification	46L54; 60H05; 60H07; 60H30
4.	Description	Abstract	In 2005, Nualart and Peccati showed that, surprisingly, the convergence in distribution of a normalized sequence of multiple Wiener-Itô integrals towards a standard Gaussian law is equivalent to convergence of just the fourth moment to 3. Recently, this result is extended to a sequence of multiple Wigner integrals, in the context of free Brownian motion. The goal of the present paper is to offer an elementary, unifying proof of these two results. The only advanced, needed tool is the product formula for multiple integrals. Apart from this formula, the rest of the proof only relies on soft combinatorial arguments.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	ANR
7.	Date	(YYYY-MM-DD)	2011-08-28
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1642
10.	Identifier	Digital Object Identifier	10.1214/ECP.v16-1642
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 16
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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