An intermediate Baum-Katz theorem

DOI10.1016/j.spl.2011.05.008zbMath1231.60021OpenAlexW2149340050MaRDI QIDQ634567

Ulrich Stadtmüller, Allan Gut

Publication date: 16 August 2011

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spl.2011.05.008

zbMATH Keywords

convergence ratesrandom fieldslaws of large numberssums of i.i.d. random variables

Mathematics Subject Classification ID

Random fields (60G60) Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Strong limit theorems (60F15)

Related Items (14)

Complete convergence and complete moment convergence for negatively associated sequences of random variables ⋮ Convergence rates in the law of large numbers and new kinds of convergence of random variables ⋮ Convergence rate in the Petrov SLLN for dependent random variables ⋮ On the convergence for PNQD sequences with general moment conditions ⋮ An extension of the Baum-Katz theorem to i.i.d. random variables with general moment conditions ⋮ Toeplitz lemma, complete convergence, and complete moment convergence ⋮ A Baum-Katz theorem for i.i.d. random variables with higher order moments ⋮ Complete moment convergence for negatively dependent sequences of random variables ⋮ Complete moment convergence for i.i.d. random variables ⋮ Complete and complete moment convergence for i.i.d. random variables under exponential moment conditions ⋮ Theorems of complete convergence and complete integral convergence for END random variables under sub-linear expectations ⋮ On the strong convergence of weighted sums of widely dependent random variables ⋮ Complete convergence and complete moment convergence for negatively dependent random variables under sub-linear expectations ⋮ Equivalent conditions of complete moment convergence for extended negatively dependent random variables

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