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Almost sure central limit theory for products of sums of partial sums. (English) Zbl 1265.60065

Summary: The aim of this paper is to consider a sequence of i.i.d. positive random variables. A universal result in an almost sure limit theorem for products of sums of partial sums is established. We show that the almost sure limit theorem holds under a fairly general conditions on the weight \(d_k=k^{-1}\exp(\ln^\beta k),\;0\leq \beta<1\). And, in a sense, our results reach the optimal form.

MSC:

60F15 Strong limit theorems
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