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arXiv · 1112.5070

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

Ivan Nourdin·Jan Rosiński
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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. 2014-02-25. Asymptotic independence of multiple Wiener-Itô integrals and the resulting limit laws. https://doi.org/10.1214/12-aop826

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