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Theory of Probability and Mathematical Statistics

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Representations and properties of weight functions in Tauberian theorems


Author: B. M. Klykavka
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 77 (2007).
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
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. A. Ya. Olenko, A Tauberian theorem for fields with the $ OR$ spectrum. II, Teor. Ĭmovır. Mat. Stat. 74 (2006), 81-97; English transl. in Theory Probab. Math. Statist. 74 (2007), 93-111. MR 2336781 (2008i:60085)
  • 2. 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
  • 3. 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)
  • 4. M. I. Yadrenko, Spectral Theory of Random Fields, ``Vyshcha Shkola'', Kiev, 1980; English transl., Optimization Software, Inc., Publications Division, New York, 1983. MR 590889 (82e:60001)
  • 5. A. Ya. Olenko and B. M. Klykavka, Some properties of weight functions in Tauberian theorems I, Theory Stoch. Process. 12(28) (2006), no. 3-4, 123-136. MR 2316570
  • 6. A. Ya. Olenko, Upper bound on $ \sqrt{x}J_\nu(x)$ and its application, Integral Transforms Spec. Funct. 17 (2006), no. 6, 455-467. MR 2238583 (2008c:33003)
  • 7. G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, 1995. MR 1349110 (96i:33010)
  • 8. A. Erdelyi, W. Magnus, F. Oberhettinger, and F. Tricomi, Higher Transcendental Functions, vol. 1, Mc.Graw-Hill, New York, Toronto, London, 1953. MR 0058756 (15:419i)
  • 9. A. Erdelyi, W. Magnus, F. Oberhettinger, and F. Tricomi, Tables of Integral Transforms, vol. 1, McGraw-Hill, New York, Toronto, London, 1954. MR 0061695 (15:868a)

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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

DOI: https://doi.org/10.1090/S0094-9000-09-00748-0
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

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