The law of the iterated logarithm for subsequences and characterization of the cluster set of \(S_{n_ k}/(2n_ k\log \,\log \,n_ k)^{1/2}\) in Banach spaces

DOI10.1007/BF01054021zbMath0674.60012OpenAlexW2040014630MaRDI QIDQ1121583

Marek Slaby

Publication date: 1989

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01054021

zbMATH Keywords

compact laws of the iterated logarithm

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Strong limit theorems (60F15) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Cites Work

• Some limit theorems for empirical processes (with discussion)
• A new proof of the Hartman-Wintner law of the iterated logarithm
• Characterization of the law of the iterated logarithm in Banach spaces
• Exponential moments of vector valued random series and triangular arrays
• When is the cluster set of S//n/\(a_ n\) empty?
• Some results on the LIL in Banach space with applications to weighted empirical processes
• Some results on the cluster set \(C(\{S_n/a_n\})\) and the LIL
• Limit theorems for moving averages of independent random vectors
• Exponential Bounds for Large Deviations
• Sums of independent Banach space valued random variables
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