A supplement to the Baum-Katz-Spitzer complete convergence theorem

DOI10.1007/s10114-005-0823-yzbMath1131.60002OpenAlexW2045326640MaRDI QIDQ884932

Andrew Rosalsky, Fu Xing Zhang, De Li Li

Publication date: 7 June 2007

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-005-0823-y

zbMATH Keywords

almost sure convergenceBaum-Katz-Spitzer complete convergence theorempartial sums of i.i.d. Banach space valued random variables

Mathematics Subject Classification ID

Strong limit theorems (60F15) Large deviations (60F10) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (3)

On the relationship between the Baum-Katz-Spitzer complete convergence theorem and the law of the iterated logarithm ⋮ On the strong approximation of the non-overlapping \(k\)-spacings process with application to the moment convergence rates ⋮ Asymptotic results for hybrids of empirical and partial sums processes

Cites Work

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• Convergence rates for probabilities of moderate deviations for sums of random variables with multidimensional indices
• Inequalities for B-valued random vectors with applications to the strong law of large numbers
• Some results on two-sided LIL behavior
• A Combinatorial Lemma and Its Application to Probability Theory
• Tail probabilities for sums of independent Banach space valued random variables
• Convergence Rates in the Law of Large Numbers

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