Refined Baum–Katz laws for weighted sums of iid random variables

Abstract We consider weighted sums ∑ k p nk X k with iid random variables ( X n ) and compare the tail probabilities of these sums with the moment conditions on X 1 . If X 1 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 p nk originating from summability are discussed.