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2007 Stable convergence of generalized $L^2$ stochastic integrals and the principle of conditioning
Peccati Giovanni, Murad Taqqu
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Electron. J. Probab. 12: 447-480 (2007). DOI: 10.1214/EJP.v12-404

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.

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Peccati Giovanni. Murad Taqqu. "Stable convergence of generalized $L^2$ stochastic integrals and the principle of conditioning." Electron. J. Probab. 12 447 - 480, 2007. https://doi.org/10.1214/EJP.v12-404

Information

Accepted: 13 April 2007; Published: 2007
First available in Project Euclid: 1 June 2016

zbMATH: 1139.60024
MathSciNet: MR2299924
Digital Object Identifier: 10.1214/EJP.v12-404

Subjects:
Primary: 60G60
Secondary: 60F05 , 60G57

Keywords: Decoupling , Generalized stochastic integrals , Independently scattered measures , multiple Poisson integrals , Principle of conditioning , Resolutions of the identity , Skorohod integrals , stable convergence , weak convergence

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