Zy. Lin et Qm. Shao, ON THE LIMITING BEHAVIORS OF INCREMENTS OF SUMS OF RANDOM-VARIABLES WITHOUT MOMENT CONDITIONS, Chinese annals of mathematics. Ser. B, 14(3), 1993, pp. 307-318
The a.s. limiting behaviors of big increments of partial sums of a seq
uence of random variables are obtained without moment conditions.The t
heorems sharpen the results of Lin[5].