Some results on two-sided LIL behavior
Some results on two-sided LIL behavior
Let {X,Xn;n≥1} be a sequence of i.i.d. mean-zero random variables, and let Sn=∑i=1nXi,n≥1. We establish necessary and sufficient conditions for having with probability 1, 0<lim sup n→∞|Sn|/$\sqrt{nh(n)}$<∞, where h is from a suitable subclass of the positive, nondecreasing slowly varying functions. Specializing our result to h(n)=(loglogn)p, where p>1 and to …