The Annals of Probability

Asymptotic independence of multiple Wiener–Itô integrals and the resulting limit laws

Ivan Nourdin and Jan Rosiński

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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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Ann. Probab., Volume 42, Number 2 (2014), 497-526.

First available in Project Euclid: 24 February 2014

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Primary: 60F05: Central limit and other weak theorems 60G15: Gaussian processes 60H05: Stochastic integrals 60H07: Stochastic calculus of variations and the Malliavin calculus

Multiple Wiener–Itô integral multiplication formula limit theorems


Nourdin, Ivan; Rosiński, Jan. Asymptotic independence of multiple Wiener–Itô integrals and the resulting limit laws. Ann. Probab. 42 (2014), no. 2, 497--526. doi:10.1214/12-AOP826.

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