Tauberian theorems for random fields with an $OR$ spectrum. I
Author:
A. Ya. Olenko
Translated by:
Oleg Klesov
Journal:
Theor. Probability and Math. Statist. 73 (2006), 135-149
MSC (2000):
Primary 60G60, 62E20, 40E05; Secondary 60F05, 26A12, 44A15
DOI:
https://doi.org/10.1090/S0094-9000-07-00688-6
Published electronically:
January 17, 2007
MathSciNet review:
2213848
Full-text PDF Free Access
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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.
References
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References
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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
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
