The Annals of Probability

When is the Cluster Set of $S_n/a_n$ Empty?

J. Kuelbs

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Abstract

We investigate the relationship between the bounded law of the iterated logarithm and the compact law of the iterated logarithm for Banach space valued random variables through the cluster set of $S_n/a_n$. Some rate of escape questions are also examined.

Article information

Source
Ann. Probab., Volume 9, Number 3 (1981), 377-394.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994412

Digital Object Identifier
doi:10.1214/aop/1176994412

Mathematical Reviews number (MathSciNet)
MR614624

Zentralblatt MATH identifier
0459.60005

JSTOR
links.jstor.org

Subjects
Primary: 60B05: Probability measures on topological spaces
Secondary: 60B10: Convergence of probability measures 60F10: Large deviations 28A40

Keywords
Law of the iterated logarithm cluster set central limit theorem rates of escape

Citation

Kuelbs, J. When is the Cluster Set of $S_n/a_n$ Empty?. Ann. Probab. 9 (1981), no. 3, 377--394. doi:10.1214/aop/1176994412. https://projecteuclid.org/euclid.aop/1176994412


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