Non-central limit theorems for random fields subordinated to gamma-correlated random fields

Leonenko, Nikolai ORCID: https://orcid.org/0000-0003-1932-4091, Ruiz-Medina, M. Dolores and Taqqu, Murad S. 2017. Non-central limit theorems for random fields subordinated to gamma-correlated random fields. Bernoulli 23 (4B) , pp. 3469-3507. 10.3150/16-BEJ853

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Abstract

A reduction theorem is proved for functionals of Gamma-correlated random fields with long-range dependence in dd-dimensional space. As a particular case, integrals of non-linear functions of chi-squared random fields, with Laguerre rank being equal to one and two, are studied. When the Laguerre rank is equal to one, the characteristic function of the limit random variable, given by a Rosenblatt-type distribution, is obtained. When the Laguerre rank is equal to two, a multiple Wiener–Itô stochastic integral representation of the limit distribution is derived and an infinite series representation, in terms of independent random variables, is obtained for the limit.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Bernoulli Society for Mathematical Statistics and Probability
ISSN:	1350-7265
Date of First Compliant Deposit:	4 October 2017
Date of Acceptance:	4 April 2016
Last Modified:	14 Nov 2024 17:00
URI:	https://orca.cardiff.ac.uk/id/eprint/89628

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