U. Einmahl et V. Goodman, CLUSTERING BEHAVIOR OF FINITE VARIANCE PARTIAL SUM PROCESSES, Probability theory and related fields, 102(4), 1995, pp. 547-565
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.