Non-central limit theorems for random fields subordinated to gamma-correlated random fields

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

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arXiv · 1504.00813

Non-central limit theorems for random fields subordinated to gamma-correlated random fields

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

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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.

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BibTeX RIS

N. N. Leonenko, M. D. Ruiz-Medina, M. S. Taqqu. 2015-04-03. Non-central limit theorems for random fields subordinated to gamma-correlated random fields. https://arxiv.org/abs/1504.00813

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