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Theory of Probability and Mathematical Statistics

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Abelian and Tauberian theorems for random fields on two-point homogeneous spaces


Author: A. A. Malyarenko
Translated by: The author
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 69 (2003).
Journal: Theor. Probability and Math. Statist. 69 (2004), 115-127
MSC (2000): Primary 60G60, 60G10; Secondary 40E05
Published electronically: February 8, 2005
MathSciNet review: 2110910
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider centered mean-square continuous random fields for which the variance of increments between two points depends only on the distance between these points. Relations between the asymptotic behavior of the variance of increments near zero and the asymptotic behavior of the spectral measure of the field near infinity are investigated. We prove several Abelian and Tauberian theorems in terms of slowly varying functions.


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Additional Information

A. A. Malyarenko
Affiliation: International Mathematical Centre, National Academy of Sciences of Ukraine
Address at time of publication: Mälardalen University, P. O. Box 883, SE–721 23 Västerås, Sweden
Email: anatoliy.malyarenko@mdh.se

DOI: https://doi.org/10.1090/S0094-9000-05-00619-8
Keywords: Random field, Abelian theorem, Tauberian theorem, two-point homogeneous space
Received by editor(s): January 3, 2003
Published electronically: February 8, 2005
Additional Notes: This work is supported in part by the Foundation for Knowledge and Competence Development.
Article copyright: © Copyright 2005 American Mathematical Society