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November 2017 Non-central limit theorems for random fields subordinated to gamma-correlated random fields
Nikolai Leonenko, M. Dolores Ruiz-Medina, Murad S. Taqqu
Bernoulli 23(4B): 3469-3507 (November 2017). DOI: 10.3150/16-BEJ853

Abstract

A reduction theorem is proved for functionals of Gamma-correlated random fields with long-range dependence in $d$-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.

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Nikolai Leonenko. M. Dolores Ruiz-Medina. Murad S. Taqqu. "Non-central limit theorems for random fields subordinated to gamma-correlated random fields." Bernoulli 23 (4B) 3469 - 3507, November 2017. https://doi.org/10.3150/16-BEJ853

Information

Received: 1 January 2015; Revised: 1 January 2016; Published: November 2017
First available in Project Euclid: 23 May 2017

zbMATH: 06778293
MathSciNet: MR3654813
Digital Object Identifier: 10.3150/16-BEJ853

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability

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Vol.23 • No. 4B • November 2017
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