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Tauberian theorems for random fields with an  spectrum. I
Author(s):
A.
Ya.
Olenko
Translated by:
Oleg Klesov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 73
(2005).
Journal:
Theor. Probability and Math. Statist.
No. 73
(2006),
135-149.
MSC (2000):
Primary 60G60, 62E20, 40E05;
Secondary 60F05, 26A12, 44A15
Posted:
January 17, 2007
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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  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:
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):
1/FEB/2005
Posted:
January 17, 2007
Additional Notes:
Supported by the NATO grant # SA(PST.CLG.976361)5437
Copyright of article:
Copyright
2007,
American Mathematical Society
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