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International Journal of Mathematics and Mathematical Sciences
Volume 17, Issue 2, Pages 323-340
http://dx.doi.org/10.1155/S0161171294000463

On Feller's criterion for the law of the iterated logarithm

1Institute of Mathematics, Jilin University, Changchun 130023, China
2Department of Mathematics & Statistics, University of Regina, Saskatchewan, Regina S4S 0A2, Canada
3Department of Statistics, North Dakota State University, Fargo, ND 58105, USA
4Department of Mathematics, Jilin University, Changchun 130023, China

Received 4 February 1992; Revised 12 February 1993

Copyright © 1994 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Combining Feller's criterion with a non-uniform estimate result in the context of the Central Limit Theorem for partial sums of independent random variables, we obtain several results on the Law of the Iterated Logarithm. Two of these results refine corresponding results of Wittmann (1985) and Egorov (1971). In addition, these results are compared with the corresponding results of Teicher (1974), Tomkins (1983) and Tomkins (1990)