Lanzinger, H.; Stadtmüller, U. - In: Stochastic Processes and their Applications 86 (2000) 2, pp. 307-322
We consider partial sums of i.i.d. random variables with moments E(X1)=0, E(X12)=[sigma]2 and and show thatwith some explicit function [phi](·). A related result for random variables with exponentially thin tails has recently been shown by Steinebach, extending a result given by Shao.