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

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)

Keywords

• central limit theorem
• Feller's criterion
• law of the iterated logarithm
• non-uniform estimates in the central limit theorem.