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arXiv · 1501.02247

Rosenblatt distribution subordinated to gaussian random fields with long-range dependence

N. N. Leonenko·M. D. Ruiz-Medina·M. S. Taqqu
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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.

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N. N. Leonenko, M. D. Ruiz-Medina, M. S. Taqqu. 2015-01-09. Rosenblatt distribution subordinated to gaussian random fields with long-range dependence. https://arxiv.org/abs/1501.02247

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