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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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.

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

First available in Project Euclid: 5 March 2002

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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]

Cluster sets generalized Banach space LIL


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.

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