LAW OF THE ITERATED LOGARITHM - CLUSTER POINTS OF
DETERMINISTIC AND RANDOM SUBSEQUENCES
Abstract: Let be a sequence of i.i.d. random variables with mean and finite,
positive variance and let
Further, let
where
is a strictly increasing subsequence of the positive integers. Then the
set of cluster points of
equals
a.s. if
and
a.s. if
These
results are then applied to randomly indexed partial sums.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -