Baum--Katz laws for certain weighted sums of independent and identically distributed random variables

Abstract

We consider weighted sums $\\sum_k p_{nk}\\, X_k$ of independent and identically\ndistributed random variables $(X_n)$ and compare the tail probabilities of these sums with\nthe moment conditions on $X_1$, that is, we prove various results of Baum--Katz type. Some\nspecial examples of weights $p_{nk}$ originating from summability are discussed.