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Theory of Probability and Mathematical Statistics

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The complete convergence in the strong law of large numbers for double sums indexed by a sector with function boundaries


Authors: K.-H. Indlekofer and O. I. Klesov
Translated by: The authors
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 68 (2003).
Journal: Theor. Probability and Math. Statist. 68 (2004), 49-53
MSC (2000): Primary 60F15
DOI: https://doi.org/10.1090/S0094-9000-04-00591-5
Published electronically: May 11, 2004
MathSciNet review: 2000394
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Abstract | References | Similar Articles | Additional Information

Abstract: We find necessary and sufficient conditions for the complete convergence in the strong law of large numbers for double sums of independent identically distributed random variables indexed by a sector with function boundaries.


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

  • 1. P. Erdös, On a theorem of Hsu and Robbins, Ann. Math. Statist. 20 (1949), 286-291; 21 (1951), 138. MR 11:40f; MR 11:375b
  • 2. D. Kh. Fuk and S. V. Nagaev, Probability inequalities for sums of independent random variables, Theory Probab. Appl. 16 (1971), 643-660; 21 (1976), 875. MR 45:2772; MR 58:24490
  • 3. A. Gut, Strong laws for independent identically distributed random variables indexed by a sector, Ann. Probab. 11 (1983), 569-577. MR 85a:60036
  • 4. A. Gut and A. Spataru, Precise asymptotics in the law of iterated logarithm, Ann. Probab. 28 (2000), 1870-1883. MR 2001m:60100
  • 5. P. L. Hsu and H. Robbins, Complete convergence and the law of large numbers, Proc. Nat. Acad. Sci. U.S.A. 33 (1947), 25-31. MR 8:470e
  • 6. O. I. Klesov, The convergence of series of probabilities of large deviations, Ukr. Math. J. 45 (1994), 845-862. MR 96e:60046
  • 7. R. Smythe, The sums of independent random variables on the partially ordered sets, Ann. Probab. 2 (1974), 906-917. MR 50:11429

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Additional Information

K.-H. Indlekofer
Affiliation: Universität Paderborn, Fachbereich Mathematik und Informatik, Warburger St. 100, 33098 Paderborn, Germany
Email: k-heinz@mathematik.uni-paderborn.de

O. I. Klesov
Affiliation: Department of Probability Theory and Mathematical Analysis, National Technical University of Ukraine, Pr. Peremogy 37, Kiev 02056, Ukraine
Email: oleg@tbimc.freenet.kiev.ua

DOI: https://doi.org/10.1090/S0094-9000-04-00591-5
Received by editor(s): April 4, 2002
Published electronically: May 11, 2004
Additional Notes: Supported in part by DFG grant 436 UKR 113/41/0.
Dedicated: Dedicated to M. I. Yadrenko on his 70th birthday.
Article copyright: © Copyright 2004 American Mathematical Society

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