A Lower Bound in a Law of the Iterated Logarithm for Sums of Symmetric and Independent Random Variables

Abstract

The law of the iterated logarithm for tail sum, abbreviated Tail LIL, was first introduced by R.Salem and S. Zygmund for sums of lacunary series. Tow and Teicher later introduced a corresponding result for independent random variables. Our article takes a different approach and focuses on obtaining one sided Tail LIL for the sums of independent and identically distributed symmetric random variables.