Work

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

Year: 2014

Type: article

Abstract: 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.

Source: The Annals of Probability

DOI: 10.1214/12-aop826

Authors: Ivan Nourdin, Jan Rosiński

Institutions: Institut Élie Cartan de Lorraine, University of Tennessee at Knoxville, Université de Lorraine

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: bronze

Funders: Université de Lorraine, Agence Nationale de la Recherche

Awards: MAlliavin, STEin, Random Irregular Equations, Visualisation of chromatin dynamics during early mammalian embryogenesis, G7240651115