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: | 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: | 25 Nov 2024 16:45 |
| URI: | https://orca.cardiff.ac.uk/id/eprint/94049 |
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