Esseen, Carl-Gustav; Janson, Svante - In: Stochastic Processes and their Applications 19 (1985) 1, pp. 173-182
Let X1, X2,... be a sequence of i.i.d. random variables and Sn their partial sums. Necessary and sufficient conditions are given for {n-1/qSn}[is proportional to]1 to have uniformly bounded pth moments, 0<p<q[less-than-or-equals, slant]2. Some of the results are generalized to martingle differences.