Extreme values and the law of the iterated logarithm

DOI10.1007/BF00699094zbMath0586.60009MaRDI QIDQ1071365

Michel Ledoux, James Kuelbs

Publication date: 1987

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

zbMATH Keywords

extreme valueslaw of the iterated logarithmcluster setdomain of attraction of a Gaussian random variable

Mathematics Subject Classification ID

Probability measures on topological spaces (60B05) Strong limit theorems (60F15) Large deviations (60F10) Convergence of probability measures (60B10) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Probability theory on linear topological spaces (60B11) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (8)

The influence of extremes on the law of the iterated logarithm ⋮ Non-classical law of the iterated logarithm behaviour for trimmed sums ⋮ Another view of the CLT in Banach spaces ⋮ Bounded and compact laws of the logarithm for \(B\)-valued random variables ⋮ A law of the iterated logarithm for distributions in the generalized domain of attraction of a nondegenerate Gaussian law ⋮ Strong approximation theorems for sums of random variables when extreme terms are excluded ⋮ Extreme values and a Gaussian central limit theorem ⋮ Limit law of the iterated logarithm for \(B\)-valued trimmed sums

Cites Work

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• Some results on the LIL in Banach space with applications to weighted empirical processes
• A strong convergence theorem for Banach space valued random variables
• Some results on the cluster set \(C(\{S_n/a_n\})\) and the LIL
• The strong law of large numbers when extreme terms are excluded from sums
• Stability for sums of i.i.d. random variables when extreme terms are excluded
• Convergence of moments and related functional in the general central limit theorem in banach spaces
• [https://portal.mardi4nfdi.de/wiki/Publication:4181018 Relation entre th�or�me central-limite et loi du logarithme it�r� dans les espaces de Banach]
• Sums of independent Banach space valued random variables

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