Rosenblatt distribution subordinated to gaussian random fields with long-range dependence
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 given, the asymptotic behavior of the eigenvalues, its L\`evy-Khintchine representation, as well as its membership to the Thorin subclass of self-decomposable distributions. The existence and boundedness of its probability density is then a direct consequence.
Cite
@article{arxiv.1501.02247,
title = {Rosenblatt distribution subordinated to gaussian random fields with long-range dependence},
author = {N. N. Leonenko and M. D. Ruiz-Medina and M. S. Taqqu},
journal= {arXiv preprint arXiv:1501.02247},
year = {2016}
}
Comments
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