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: -