Asymptotic independence of multiple Wiener-Itô integrals and the resulting limit laws
نویسندگان
چکیده
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.
منابع مشابه
Convergence in variation of the joint laws of multiple Wiener–Itô integrals
The convergence in variation of the laws of multiple Wiener–Itô integrals with respect to their kernel has been studied by Davydov and Martynova in [1987. Limit behavior of multiple stochastic integral. Statistics and Control of Random Process (Preila, 1987), Nauka, Moscow, pp. 55–57 (in Russian)]. Here, we generalize this convergence for the joint laws of multiple Wiener–Itô integrals. In this...
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