Tauberian theorem for fields with an spectrum. II

Author:
A. Ya. Olenko

Translated by:
V. V. Semenov

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **74** (2006).

Journal:
Theor. Probability and Math. Statist. **74** (2007), 93-111

MSC (2000):
Primary 60G60, 62E20, 40E05; Secondary 60F05, 26A12, 44A15

DOI:
https://doi.org/10.1090/S0094-9000-07-00700-4

Published electronically:
June 29, 2007

MathSciNet review:
2336781

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We consider homogeneous isotropic random fields whose spectra have some local singular properties. We prove Abelian and Tauberian theorems linking the local behavior of the spectral function and that of weighted integral functionals of random fields. Representations of weight functions in the form of the Hankel transform and series of functions are obtained. The asymptotic behavior is described in terms of functions of the class . Some examples are given.

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Additional Information

**A. Ya. Olenko**

Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Volodymyrs’ka Street, 64, Kyiv 01033, Ukraine

Email:
olenk@univ.kiev.ua

DOI:
https://doi.org/10.1090/S0094-9000-07-00700-4

Keywords:
Tauberian theorem,
Abelian theorem,
slowly varying functions,
$OR$ class of functions,
random fields,
homogeneous fields,
isotropic fields,
functionals of a random field,
spectral function,
correlation function,
asymptotics,
strong dependence,
Hankel transform,
Bessel functions

Received by editor(s):
February 1, 2005

Published electronically:
June 29, 2007

Article copyright:
© Copyright 2007
American Mathematical Society