ASYMPTOTIC INDEPENDENCE OF MULTIPLE WIENER-ITO INTEGRALS AND THE RESULTING LIMIT LAWS

• 成果类型: Article
• 署名作者: Nourdin, Ivan; Rosinski, Jan
• 署名单位: Universite de Lorraine; University of Tennessee System; University of Tennessee Knoxville
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/12-AOP826
• 发表日期: 2014
• 页码: 497-526
• 关键词: theorems; CONVERGENCE; functionals

摘要

We characterize the asymptotic independence between blocks consisting of multiple Wiener-Ito 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-Ito 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.