# Refined Baum-Katz laws for weighted sums of iid random variables

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## Abstract

We consider weighted sums with iid random variables (Xn) and compare the tail probabilities of these sums with the moment conditions on X1. If X1 is in the domain of attraction of a stable law then refined Baum-Katz laws generalizing results of Heyde, Gut and other authors are presented. Some special examples of weights pnk originating from summability are discussed.

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