On the Hsu-Robbins-Erdős-Spitzer-Baum-Katz theorem for random fields

DOI10.1016/j.jmaa.2011.09.010zbMath1231.60022OpenAlexW2161380802MaRDI QIDQ645407

Allan Gut, Ulrich Stadtmüller

Publication date: 15 November 2011

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.09.010

zbMATH Keywords

convergence rateslaw of large numberslaw of the iterated logarithmrandom fieldssums of i.i.d. random variableslast exit time

Mathematics Subject Classification ID

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

Related Items (8)

Some strong limit theorems for weighted sums of measurable operators ⋮ On the convergence rates in the asymmetric SLLN for independent and nonidentically distributed random fields ⋮ The Hsu-Robbins-Erdös theorem for the maximum partial sums of quadruplewise independent random variables ⋮ On the strong approximation of the non-overlapping \(k\)-spacings process with application to the moment convergence rates ⋮ On Rio's proof of limit theorems for dependent random fields ⋮ On the necessary condition for Baum-Katz type theorem for non-identically distributed and negatively dependent random fields ⋮ On the hybrids of \(k\)-spacing empirical and partial sum processes ⋮ An approach to complete convergence theorems for dependent random fields via application of Fuk-Nagaev inequality

Cites Work

• Laws of the single logarithm for delayed sums of random fields. II
• An asymmetric Marcinkiewicz-Zygmund LLN for random fields
• Convergence rates for probabilities of moderate deviations for sums of random variables with multidimensional indices
• Limit theorems for delayed sums
• Marcinkiewicz laws and convergence rates in the law of large numbers for random variables with multidimensional indices
• Convergence Rates in the Law of Large Numbers
• ON THE LAW OF THE ITERATED LOGARITHM
• Complete Convergence and the Law of Large Numbers
• On a Theorem of Hsu and Robbins
• Remark on my Paper "On a Theorem of Hsu and Robbins"
• Probability: A Graduate Course
• Unnamed Item

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