Tauberian and Abelian theorems for long-range dependent random fields

Nikolai Leonenko; Andriy Olenko

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arXiv · 1307.1857

Tauberian and Abelian theorems for long-range dependent random fields

Nikolai Leonenko·Andriy Olenko

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Abstract

This paper surveys Abelian and Tauberian theorems for long-range dependent random fields. We describe a framework for asymptotic behaviour of covariance functions or variances of averaged functionals of random fields at infinity and spectral densities at zero. The use of the theorems and their limitations are demonstrated through applications to some new and less-known examples of covariance functions of long-range dependent random fields.

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BibTeX RIS

Nikolai Leonenko, Andriy Olenko. 2013-07-07. Tauberian and Abelian theorems for long-range dependent random fields. https://arxiv.org/abs/1307.1857

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