International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 2, Pages 323-340
doi:10.1155/S0161171294000463
On Feller's criterion for the law of the iterated logarithm
Deli Li1
, M.Bhaskara Rao2
and Xiangchen Wang3
1Institute of Mathematics, Jilin University, Changchun 130023, China
2Department of Statistics, North Dakota State University, Fargo 58105, ND, USA
3Department of Mathematics, Jilin University, Changchun 130023, China
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)