CLUSTERING BEHAVIOR OF FINITE VARIANCE PARTIAL SUM PROCESSES

Clustering rates in Strassen's functional law of the iterated logarith m are determined for finite variance partial sum processes in one dime nsion. A general characterization of these rates, similar to one recen tly obtained for one-dimensional Brownian motion, shows that relativel y mild moment conditions on a partial sum process lead to high order c lustering rates at certain points of the Strassen set.