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

Full-text PDF

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.

**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**

Retrieve articles in *Theory of Probability and Mathematical Statistics*
with MSC (2000):
60F15

Retrieve articles in all journals with MSC (2000): 60F15

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