Abstract
We consider weighted sums $\sum_k p_{nk}\, X_k$ of independent and identically distributed random variables $(X_n)$ and compare the tail probabilities of these sums with the moment conditions on $X_1$, that is, we prove various results of Baum--Katz type. Some special examples of weights $p_{nk}$ originating from summability are discussed.
Citation
Hartmut Lanzinger. Ulrich Stadtmüller. "Baum--Katz laws for certain weighted sums of independent and identically distributed random variables." Bernoulli 9 (6) 985 - 1002, December 2003. https://doi.org/10.3150/bj/1072215198
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