Non-central limit theorems for random fields subordinated to gamma-correlated random fields
Spectral Theory
2015-04-06 v1 Probability
Abstract
A reduction theorem is proved for functionals of Gamma-correlated random fields with long-range dependence in d-dimensional space. In the particular case of a non-linear function of a chi-squared random field with Laguerre rank equal to one, we apply the Karhunen-Lo\'eve expansion and the Fredholm determinant formula to obtain the characteristic function of its Rosenblatt-type limit distribution. When the Laguerre rank equals one and two, we obtain the multiple Wiener-It\^o stochastic integral representation of the limit distribution. In both cases, an infinite series representation in terms of independent random variables is constructed for the limit random variables.
Cite
@article{arxiv.1504.00813,
title = {Non-central limit theorems for random fields subordinated to gamma-correlated random fields},
author = {N. N. Leonenko and M. D. Ruiz-Medina and M. S. Taqqu},
journal= {arXiv preprint arXiv:1504.00813},
year = {2015}
}