LAW OF THE ITERATED LOGARITHM FOR SUBSEQUENCES

Abstract: Let denote the partial sums of i.i.d. random variables with mean The
present paper investigates the quantity

where

is a strictly increasing subsequence of the positive integers. The first results
are that if

then the limit superior equals

a.s. for subsequences which
increase ”at most geometrically”, and

where

for
subsequences which increase ”at least geometrically”. We also perform a refined analysis for
the latter case and finally present criteria for the finiteness of

in
both cases.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -