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

DOI10.1016/J.SPL.2004.06.033zbMath1074.60039OpenAlexW2035773285MaRDI QIDQ1771473

Ulrich Stadtmüller, Hartmut Lanzinger

Publication date: 21 April 2005

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

Full work available at URL: https://doi.org/10.1016/j.spl.2004.06.033

zbMATH Keywords

tail probabilities

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Strong limit theorems (60F15)

Related Items (12)

REFINEMENT OF CONVERGENCE RATES FOR WEIGHTED SUMS OF INDEPENDENT RANDOM VARIABLES ⋮ Precise asymptotics in the law of the logarithm for random fields in Hilbert space ⋮ A general law of moment convergence rates for uniform empirical process ⋮ A supplement to the convergence rate in a theorem of Heyde ⋮ A kind of complete moment convergence for self-normalized sums ⋮ Complete convergence and complete moment convergence for maximal weighted sums of arrays of rowwise extended negatively dependent random variables with statistical applications ⋮ Asymptotic property for some series of probability ⋮ A kind of complete moment convergence for sums of independent and nonidentically distributed random variables ⋮ Precise asymptotics for complete moment convergence of \(U\)-statistics of i.i.d. random variables ⋮ A general pattern of asymptotic behavior of the \(R/S\) statistics for linear processes ⋮ A general law of complete moment convergence for self-normalized sums ⋮ Exact rates in complete moment convergence of self-normalized sums for multidimensionally indexed random variables

Cites Work

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• Weighted sums of random variables attracted to stable laws
• Complete convergence and Cesàro summation for i.i.d. random variables
• Baum-Katz laws for certain weighted sums of independent and identically distributed random variables
• Complete convergence for weighted sums of negatively associated random variables
• Precise asymptotics in the Baum-Katz and Davis laws of large numbers
• Complete convergence for weighted sums of NA sequences
• A supplement to the strong law of large numbers
• Convergence Rates in the Law of Large Numbers
• Sums of independent Banach space valued random variables

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