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Theory of Probability and Mathematical Statistics

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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
Published electronically: January 20, 2011
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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

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

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

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