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Gaussian Approximations of Multiple Integrals

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Gaussian Approximations of Multiple Integrals
2.	Creator	Author's name, affiliation, country	Giovanni Peccati; Université Paris VI
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Gaussian processes; Malliavin calculus; Multiple stochastic integrals; Non-central limit theorems; Weak convergence
3.	Subject	Subject classification	60F05; 60G15; 60H05; 60H07
4.	Description	Abstract	Fix $k\geq 1$, and let $I(l), l \geq 1$, be a sequence of $k$-dimensional vectors of multiple Wiener-Itô integrals with respect to a general Gaussian process. We establish necessary and sufficient conditions to have that, as $l \to\infty$, the law of $I(l)$ is asymptotically close (for example, in the sense of Prokhorov's distance) to the law of a $k$-dimensional Gaussian vector having the same covariance matrix as $I(l)$. The main feature of our results is that they require minimal assumptions (basically, boundedness of variances) on the asymptotic behaviour of the variances and covariances of the elements of $I(l)$. In particular, we will not assume that the covariance matrix of $I(l)$ is convergent. This generalizes the results proved in Nualart and Peccati (2005), Peccati and Tudor (2005) and Nualart and Ortiz-Latorre (2007). As shown in Marinucci and Peccati (2007b), the criteria established in this paper are crucial in the study of the high-frequency behaviour of stationary fields defined on homogeneous spaces.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	ISI Foundation -- Lagrange Project
7.	Date	(YYYY-MM-DD)	2007-10-13
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/1322
10.	Identifier	Digital Object Identifier	10.1214/ECP.v12-1322
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 12
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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