SOME UNIVERSAL RESULTS ON THE BEHAVIOR OF INCREMENTS OF PARTIAL-SUMS

We establish very general one-sided results on the lim sup behavior of increments of suitably normalized partial sums of i.i.d. random varia bles. Our main results apply to arbitrary nondegenerate positive rando m variables which need not have any finite moments. As a corollary we can show that such results also hold for not necessarily positive rand om variables whose negative parts have finite moment-generating functi ons.