English

Tauberian and Abelian theorems for long-range dependent random fields

Probability 2013-07-09 v1

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

Cite

@article{arxiv.1307.1857,
  title  = {Tauberian and Abelian theorems for long-range dependent random fields},
  author = {Nikolai Leonenko and Andriy Olenko},
  journal= {arXiv preprint arXiv:1307.1857},
  year   = {2013}
}

Comments

Will appear in Methodology and Computing in Applied Probability. 26 pages, 10 figures. The final publication is available at link.springer.com. DOI: 10.1007/s11009-012-9276-9

R2 v1 2026-06-22T00:46:51.233Z