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

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

2011-12-21

arxiv.org/abs/1112.5070v2

Mathematics

Probability

18 pages

Scientific paper

We characterize the asymptotic independence of multiple Wiener-It\^o
integrals. As a consequence of this characterization, we derive the celebrated
fourth moment theorem of Nualart and Peccati and other related results on the
multivariate convergence of multiple Wiener-It\^o integrals, that involve
Gaussian and non Gaussian limits.

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