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, and . 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.