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Tauberian and Abelian Theorems for Long-range Dependent Random Fields

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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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Authors and Affiliations

  1. School of Mathematics, Cardiff University, Senghennydd Road, CF24 4AG, Cardiff, UK

    Nikolai Leonenko

  2. Department of Mathematics and Statistics, La Trobe University, Bundoora, VIC, 3086, Australia

    Andriy Olenko

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  1. Nikolai Leonenko
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  2. Andriy Olenko
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Correspondence to Andriy Olenko.

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Leonenko, N., Olenko, A. Tauberian and Abelian Theorems for Long-range Dependent Random Fields. Methodol Comput Appl Probab 15, 715–742 (2013). https://doi.org/10.1007/s11009-012-9276-9

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  • DOI: https://doi.org/10.1007/s11009-012-9276-9

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