Asymptotic independence of multiple Wiener-It\^o integrals and the resulting limit laws

By Ivan Nourdin, J. Rosinski. 2011

60 citations recorded by the source corpus.

We characterize the asymptotic independence between blocks consisting of multiple Wiener-It\^{o} 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-It\^{o} 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.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3f7ca298ab9eec1e9fc4e08f22d6da4d0d72b063

Citations in the corpus

• Malliavin-Stein method for variance-gamma approximation on Wiener space (2014, unknown): “1 in [20]).”