The goal of this paper is to show that, in most strong laws of large numbers, the nth partial sum can be replaced with the largest of the first n sums. Moreover it is shown that the usual assumptions of independence and common distribution are unnecessary and that these results apply also to strong laws for Banach valued random elements.
@article{urn:eudml:doc:39003,
title = {A note on the almost sure limiting behavior of the maximun of a sequence of partial sums.},
journal = {Stochastica},
volume = {12},
year = {1988},
pages = {235-240},
zbl = {0691.60024},
mrnumber = {MR1024762},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39003}
}
Adler, André. A note on the almost sure limiting behavior of the maximun of a sequence of partial sums.. Stochastica, Tome 12 (1988) pp. 235-240. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39003/