## The Annals of Probability

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

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 24 February 2014

https://projecteuclid.org/euclid.aop/1393251294

Digital Object Identifier
doi:10.1214/12-AOP826

Mathematical Reviews number (MathSciNet)
MR3178465

Zentralblatt MATH identifier
1301.60026

#### Citation

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. https://projecteuclid.org/euclid.aop/1393251294

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