Tauberian and Abelian Theorems for Long-range Dependent Random Fields

Nikolai Leonenko () and Andriy Olenko ()
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Nikolai Leonenko: Cardiff University
Andriy Olenko: La Trobe University

Methodology and Computing in Applied Probability, 2013, vol. 15, issue 4, 715-742

Abstract: 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.

Keywords: Random field; Homogeneous random field; Covariance function; Abelian theorem; Tauberian theorem; Long-range dependence; 60G60; 62E20; 40E05 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s11009-012-9276-9

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