On an Independence Criterion for Multiple Wiener Integrals
نویسندگان
چکیده
منابع مشابه
Asymptotic independence of multiple Wiener-Itô integrals and the resulting limit laws
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 ...
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Let Fn = (F1,n, ...., Fd,n), n > 1, be a sequence of random vectors such that, for every j = 1, ..., d, the random variable Fj,n belongs to a fixed Wiener chaos of a Gaussian field. We show that, as n → ∞, the components of Fn are asymptotically independent if and only if Cov(F 2 i,n, F 2 j,n) → 0 for every i 6= j. Our findings are based on a novel inequality for vectors of multiple Wiener-Itô ...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1991
ISSN: 0091-1798
DOI: 10.1214/aop/1176990436