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March 2014 Asymptotic independence of multiple Wiener–Itô integrals and the resulting limit laws
Ivan Nourdin, Jan Rosiński
Ann. Probab. 42(2): 497-526 (March 2014). DOI: 10.1214/12-AOP826

Abstract

We characterize the asymptotic independence between blocks consisting of multiple Wiener–Itô integrals. As a consequence of this characterization, we derive the celebrated fourth moment theorem of Nualart and Peccati, its multidimensional extension and other related results on the multivariate convergence of multiple Wiener–Itô integrals, that involve Gaussian and non Gaussian limits. We give applications to the study of the asymptotic behavior of functions of short and long-range dependent stationary Gaussian time series and establish the asymptotic independence for discrete non-Gaussian chaoses.

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Ivan Nourdin. Jan Rosiński. "Asymptotic independence of multiple Wiener–Itô integrals and the resulting limit laws." Ann. Probab. 42 (2) 497 - 526, March 2014. https://doi.org/10.1214/12-AOP826

Information

Published: March 2014
First available in Project Euclid: 24 February 2014

zbMATH: 1301.60026
MathSciNet: MR3178465
Digital Object Identifier: 10.1214/12-AOP826

Subjects:
Primary: 60F05 , 60G15 , 60H05 , 60H07

Keywords: limit theorems , multiple Wiener–Itô integral , multiplication formula

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.42 • No. 2 • March 2014
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