The Annals of Probability

Cluster Sets for a Generalized Law of the Iterated Logarithm in Banch Spaces

U. Einmahl and J. Kuelbs

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Abstract

We identify the possible cluster sets for a general lawof the iterated logarithm in the Banach space setting,and showthat all the possible limit sets arise as cluster sets for some random vector in an arbitrary separable Banach space. This extends previous results obtained in .nite dimensional Euclidean spaces.

Article information

Source
Ann. Probab., Volume 29, Number 4 (2001), 1451-1475.

Dates
First available in Project Euclid: 5 March 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1015345758

Digital Object Identifier
doi:10.1214/aop/1015345758

Mathematical Reviews number (MathSciNet)
MR1880228

Zentralblatt MATH identifier
1021.60002

Subjects
Primary: 60B11: Probability theory on linear topological spaces [See also 28C20] 60B12: Limit theorems for vector-valued random variables (infinite- dimensional case) 60F15: Strong theorems
Secondary: 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11]

Keywords
Cluster sets generalized Banach space LIL

Citation

Einmahl, U.; Kuelbs, J. Cluster Sets for a Generalized Law of the Iterated Logarithm in Banch Spaces. Ann. Probab. 29 (2001), no. 4, 1451--1475. doi:10.1214/aop/1015345758. https://projecteuclid.org/euclid.aop/1015345758


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References

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