Rosenblatt distribution subordinated to Gaussian random fields with long-range dependence. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Leonenko, N. N.; Ruiz-Medina, M. D.; Taqqu, M. S.
• Is Part Of: Stochastic analysis and applications. Volume 35:Issue 1(2017)
• Page Start: 144
• Page End: 177
• Publication Date: 2017-01-02
• Subjects: Fredholm determinant -- hermite polynomials -- infinite divisible distributions -- multiple Wiener–Itô stochastic integrals -- non-central limit theorems -- Rosenblatt-type distribution; 60F99 -- 60E10 -- 60G15 -- 60G60; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2016.1230723
• Languages: English
• ISSNs: 0736-2994

Abstract

ABSTRACT: The Karhunen–Loève expansion and the Fredholm determinant formula are used to derive an asymptotic Rosenblatt-type distribution of a sequence of integrals of quadratic functions of Gaussian stationary random fields on displaying long-range dependence. This distribution reduces to the usual Rosenblatt distribution when d = 1. Several properties of this new distribution are obtained. Specifically, its series representation, in terms of independent chi-squared random variables, is established. Its Lévy–Khintchine representation, and membership to the Thorin subclass of self-decomposable distributions are obtained as well. The existence and boundedness of its probability density then follow as a direct consequence.