Almost sure central limit theory for products of sums of partial sums
Consider a sequence of i.i.d. positive random variables. An universal result in almost sure limit theorem for products of sums of partial sums is established. We will show that the almost sure limit theorem holds under a fairly general condition on the weight dk = k−1 exp(lnβk), 0 ≤ β < 1. And in a sense, our results have reached the optimal form.
Keywordsalmost sure central limit theorem weight product of sums of partial sums
MR Subject Classification60F15
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