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arXiv · 1307.3349

Asymptotic behaviour of functionals of cyclical long-range dependent random fields

Boris Klykavka·Andriy Olenko·Matthew Vicendese
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Abstract

Long-range dependent random fields with spectral densities which are unbounded at some frequencies are investigated. We demonstrate new examples of covariance functions which do not exhibit regular varying asymptotic behaviour at infinity. However, variances of averaged functionals of these fields are regularly varying. Limit theorems for weighted functionals of cyclical long-range dependent fields are obtained. The order of normalizing constants and relations between the weight functions and singularities in non-degenerative asymptotics are discussed.

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Boris Klykavka, Andriy Olenko, Matthew Vicendese. 2013-07-12. Asymptotic behaviour of functionals of cyclical long-range dependent random fields. https://doi.org/10.1007/s10958-012-1047-1

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