A note on the law of the iterated logarithm in Hilbert space

DOI10.1007/BF00354760zbMath0687.60005OpenAlexW2049795836MaRDI QIDQ1263149

Uwe Einmahl

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1007/bf00354760

zbMATH Keywords

variableslogarithmHilbert space-valued Gaussian mean-zero randomintegral test for lower and upper classeslaw of the iteratedpregaussian mean-zero random variables

Mathematics Subject Classification ID

Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (2)

Feller’s upper-lower class test in Euclidean space ⋮ Exact convergence rates for the bounded law of the iterated logarithm in Hilbert space

Cites Work

• A useful estimate in the multidimensional invariance principle
• Strong invariance principles for partial sums of independent random vectors
• Berry-Esseen estimates in Hilbert space and an application to the law of the iterated logarithm
• Exponential inequalities for sums of random vectors
• Sample path behavior for Brownian motion in Banach spaces
• The Darling-Erdős theorem for sums of i.i.d. random variables
• Some results on the cluster set \(C(\{S_n/a_n\})\) and the LIL
• The law of the iterated logarithm for identically distributed random variables
• The Integral of a Symmetric Unimodal Function over a Symmetric Convex Set and Some Probability Inequalities
• Concerning a Certain Probability Problem

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