Precise asymptotics in the self-normalized law of the iterated logarithm

Let X,X1,X2, . . . be i.i.d. nondegenerate random variables with zero means, Sn = n j=1 Xj and V 2 n = n j=1 X2 j. We investigate the precise asymptotics in the law of the iterated logarithm for self-normalized sums, Sn/Vn, also for the maximum of self-normalized sums, max1 k n |Sk|/Vn, when X belongs to the domain of attraction of the normal law. © 2007 Elsevier Inc. All rights reserved