Rosenblatt distribution subordinated to Gaussian fields with long-range dependence

Leonenko, Nikolai ORCID: https://orcid.org/0000-0003-1932-4091, 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:	https://arxiv.org/abs/1501.02247
Date of First Compliant Deposit:	26 August 2016
Date of Acceptance:	16 August 2016
Last Modified:	07 Nov 2023 07:07
URI:	https://orca.cardiff.ac.uk/id/eprint/94049

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