Non-central limit theorems for random fields subordinated to gamma-correlated random fields
Files
First author draft
Date
2017-11-01
Authors
Leonenko, Nikolai
Ruiz-Medina, M. Dolores
Taqqu, Murad S.
Version
First author draft
OA Version
Citation
Nikolai Leonenko, M. Dolores Ruiz-Medina, Murad S Taqqu. 2017. "Non-central limit theorems for random fields subordinated to gamma-correlated random fields." BERNOULLI, Volume 23, Issue 4B, pp. 3469 - 3507 (39). https://doi.org/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.