A limit theorem for random fields with a singularity in the spectrum

Authors:
A. Ya. Olenko and B. M. Klykavka

Translated by:
O. Klesov

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **81** (2010).

Journal:
Theor. Probability and Math. Statist. **81** (2010), 147-158

MSC (2010):
Primary 60G60; Secondary 60F17

DOI:
https://doi.org/10.1090/S0094-9000-2011-00816-2

Published electronically:
January 20, 2011

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Homogeneous isotropic random fields with singularities in spectra at nonzero frequencies are studied. This class of fields generalizes the case of random fields with long range dependence where the spectrum has a singularity at the origin. We obtain a limit theorem for integral weight functionals of the field. We also discuss the difference between this class and the long range dependence.

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Additional Information

**A. Ya. Olenko**

Affiliation:
Department of Mathematics and Statistics, La Trobe University, Victoria 3086, Australia

Email:
a.olenko@latrobe.edu.au

**B. M. Klykavka**

Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine

Email:
bklykavka@yahoo.com

DOI:
https://doi.org/10.1090/S0094-9000-2011-00816-2

Keywords:
Random fields,
limit theorem,
integral weight functionals,
spectral functions,
long range dependence

Received by editor(s):
August 31, 2009

Published electronically:
January 20, 2011

Additional Notes:
Supported by the Swedish Institute grant SI-01424/2007

Article copyright:
© Copyright 2011
American Mathematical Society