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Stable convergence of generalized $L^2$ stochastic integrals and the principle of conditioning

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1.	Title	Title of document	Stable convergence of generalized $L^2$ stochastic integrals and the principle of conditioning
2.	Creator	Author's name, affiliation, country	Peccati Giovanni; Université Paris VI
2.	Creator	Author's name, affiliation, country	Murad S Taqqu; Boston University
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Generalized stochastic integrals; Independently scattered measures; Decoupling; Principle of conditioning; Resolutions of the identity; Stable convergence; Weak convergence; multiple Poisson integrals; Skorohod integrals
3.	Subject	Subject classification	60G60, 60G57, 60F05
4.	Description	Abstract	We consider generalized adapted stochastic integrals with respect to independently scattered random measures with second moments, and use a decoupling technique, formulated as a «principle of conditioning», to study their stable convergence towards mixtures of infinitely divisible distributions. The goal of this paper is to develop the theory. Our results apply, in particular, to Skorohod integrals on abstract Wiener spaces, and to multiple integrals with respect to independently scattered and finite variance random measures. The first application is discussed in some detail in the final sectionof the present work, and further extended in a companion paper (Peccati and Taqqu (2006b)). Applications to the stable convergence (in particular, central limit theorems) of multiple Wiener-Itô integrals with respect to independently scattered (and not necessarily Gaussian) random measures are developed in Peccati and Taqqu (2006a, 2007). The present work concludes with an example involving quadratic Brownian functionals.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2007-04-13
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/404
10.	Identifier	Digital Object Identifier	10.1214/EJP.v12-404
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 12
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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