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arXiv · 1812.07290

Limit theorems for filtered long-range dependent random fields

Tareq Alodat·Nikolai Leonenko·Andriy Olenko
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Abstract

This article investigates general scaling settings and limit distributions of functionals of filtered random fields. The filters are defined by the convolution of non-random kernels with functions of Gaussian random fields. The case of long-range dependent fields and increasing observation windows is studied. The obtained limit random processes are non-Gaussian. Most known results on this topic give asymptotic processes that always exhibit non-negative auto-correlation structures and have the self-similar parameter $H\in(\frac{1}{2},1)$. In this work we also obtain convergence for the case $H\in(0,\frac{1}{2})$ and show how the Hurst parameter $H$ can depend on the shape of the observation windows. Various examples are presented.

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Tareq Alodat, Nikolai Leonenko, Andriy Olenko. 2018-12-18. Limit theorems for filtered long-range dependent random fields. https://arxiv.org/abs/1812.07290

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