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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

Tauberian theorems for random fields with an $ OR$ spectrum. I


Author: A. Ya. Olenko
Translated by: Oleg Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 73 (2005).
Journal: Theor. Probability and Math. Statist. 73 (2006), 135-149
MSC (2000): Primary 60G60, 62E20, 40E05; Secondary 60F05, 26A12, 44A15
Published electronically: January 17, 2007
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Abstract | References | Similar Articles | Additional Information

Abstract: We obtain Abelian and Tauberian theorems describing a relationship between the asymptotic behavior at the origin of the spectrum of a random field and that at infinity of the integral of the random field over a sphere or a ball. We consider the case of homogeneous isotropic fields with singular spectra at the origin. The asymptotic behavior is given in terms of $ OR$ functions.


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Additional Information

A. Ya. Olenko
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mathematics and Mechanics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email: olenk@univ.kiev.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-07-00688-6
PII: S 0094-9000(07)00688-6
Keywords: Tauberian theorem, Abelian theorem, slowly varying functions, $OR$ functions, random fields, homogeneous fields, isotropic fields, functionals of a random field, spectral function, correlation function, asymptotic behavior, strong dependence
Received by editor(s): February 1, 2005
Published electronically: January 17, 2007
Additional Notes: Supported by the NATO grant # SA(PST.CLG.976361)5437
Article copyright: © Copyright 2007 American Mathematical Society