The Annals of Probability

Self-Normalized Laws of the Iterated Logarithm

Philip S. Griffin and James D. Kuelbs

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Abstract

Using suitable self-normalizations for partial sums of i.i.d. random variables, a law of the iterated logarithm, which generalizes the classical LIL, is proved for all distributions in the Feller class. A special case of these results applies to any distribution in the domain of attraction of some stable law.

Article information

Source
Ann. Probab., Volume 17, Number 4 (1989), 1571-1601.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991175

Digital Object Identifier
doi:10.1214/aop/1176991175

Mathematical Reviews number (MathSciNet)
MR1048947

Zentralblatt MATH identifier
0687.60033

JSTOR
links.jstor.org

Subjects
Primary: 60F15: Strong theorems

Keywords
Law of the iterated logarithm domains of attraction self-normalization stochastic compactness

Citation

Griffin, Philip S.; Kuelbs, James D. Self-Normalized Laws of the Iterated Logarithm. Ann. Probab. 17 (1989), no. 4, 1571--1601. doi:10.1214/aop/1176991175. https://projecteuclid.org/euclid.aop/1176991175


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