Between the LIL and the LSL

Original · EN

In two earlier papers, two of the present authors (A.G. and U.S.) extended Lai's [Ann. Probab. 2 (1974) 432--440] law of the single logarithm for delayed sums to a multiindex setting in which the edges of the nth window grow like |n|α, or with different α's, where the α's belong to (0,1). In this paper, the edge of the nth window typically grows like n/ n, thus at a higher rate than any power less than one, but not quite at the LIL-rate.