Representations and properties of weight functions in Tauberian theorems
Author:
B. M. Klykavka
Translated by:
S. Kvasko
Journal:
Theor. Probability and Math. Statist. 77 (2008), 71-90
MSC (2000):
Primary 60G60, 62E20, 40E05
DOI:
https://doi.org/10.1090/S0094-9000-09-00748-0
Published electronically:
January 16, 2009
MathSciNet review:
2432773
Full-text PDF Free Access
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Abstract: We continue the studies of weight functions in Tauberian theorems for random fields. We obtain the rate of convergence of function series in the representation of a weight function and prove a recurrence relation for weight functions in spaces of various dimensions.
References
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References
- A. Ya. Olenko, A Tauberian theorem for fields with the $OR$ spectrum. II, Teor. Ĭmovīr. Mat. Stat. 74 (2006), 81–97; English transl. in Theory Probab. Math. Statist. 74 (2007), 93–111. MR 2336781 (2008i:60085)
- A. Ya. Olenko, Some properties of weight functions in Tauberian theorems. II, Theory Stoch. Process. 13(29) (2007), no. 1–2, 194–204. MR 2343823
- N. N. Leonenko and A. V. Ivanov, Statistical Analysis of Random Fields, “Vyshcha Shkola”, Kiev, 1986; English transl., Kluwer Academic Publishers Group, Dordrecht, 1989. MR 917486 (89e:62125)
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Additional Information
B. M. Klykavka
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email:
bklykavka@yahoo.com
Keywords:
Tauberian theorems,
random fields,
covariance function,
spectral function,
weight function,
rate of convergence
Received by editor(s):
December 25, 2006
Published electronically:
January 16, 2009
Article copyright:
© Copyright 2009
American Mathematical Society
