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
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
Full-text PDF Free Access
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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
- 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
- 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
- A. Gut, Strong laws for independent identically distributed random variables indexed by a sector, Ann. Probab. 11 (1983), 569–577. MR 85a:60036
- A. Gut and A. Spataru, Precise asymptotics in the law of iterated logarithm, Ann. Probab. 28 (2000), 1870–1883. MR 2001m:60100
- 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
- O. I. Klesov, The convergence of series of probabilities of large deviations, Ukr. Math. J. 45 (1994), 845–862. MR 96e:60046
- R. Smythe, The sums of independent random variables on the partially ordered sets, Ann. Probab. 2 (1974), 906–917. MR 50:11429
References
- 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
- 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
- A. Gut, Strong laws for independent identically distributed random variables indexed by a sector, Ann. Probab. 11 (1983), 569–577. MR 85a:60036
- A. Gut and A. Spataru, Precise asymptotics in the law of iterated logarithm, Ann. Probab. 28 (2000), 1870–1883. MR 2001m:60100
- 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
- O. I. Klesov, The convergence of series of probabilities of large deviations, Ukr. Math. J. 45 (1994), 845–862. MR 96e:60046
- 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
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
