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Rosenblatt distribution subordinated to Gaussian fields with long-range dependence

Leonenko, Nikolai, Ruiz-Medina, M. D. and Taqqu, M. S. 2017. Rosenblatt distribution subordinated to Gaussian fields with long-range dependence. Stochastic Analysis and Applications 35 (1) , pp. 144-177.

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Abstract

The Karhunen-Lo`eve 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 R d 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 L´evy-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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Uncontrolled Keywords: Asymptotics of eigenvalues, Fredholm determinant, Hermite polynomials, infinite divisible distributions, multiple Wiener-Itˆo stochastic integrals, non-central limit theorems, Rosenblatt-type distribution
Publisher: Taylor and Francis
ISSN: 0736-2994
Related URLs:
Date of First Compliant Deposit: 26 August 2016
Date of Acceptance: 16 August 2016
Last Modified: 08 Dec 2017 10:45
URI: http://orca.cf.ac.uk/id/eprint/94049

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