The Annals of Probability

A New Proof of the Hartman-Wintner Law of the Iterated Logarithm

Alejandro de Acosta

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Abstract

A new proof of the Hartman-Wintner law of the iterated logarithm is given. The main new ingredient is a simple exponential inequality. The same method gives a new, simpler proof of a basic result of Kuelbs on the LIL in the Banach space setting.

Article information

Source
Ann. Probab., Volume 11, Number 2 (1983), 270-276.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993596

Digital Object Identifier
doi:10.1214/aop/1176993596

Mathematical Reviews number (MathSciNet)
MR690128

Zentralblatt MATH identifier
0512.60014

JSTOR
links.jstor.org

Subjects
Primary: 60B05: Probability measures on topological spaces
Secondary: 60F05: Central limit and other weak theorems 60F10: Large deviations 60F15: Strong theorems

Keywords
Hartman-Wintner law of the iterated logarithm exponential inequality cluster set law of the iterated logarithm in Banach spaces

Citation

de Acosta, Alejandro. A New Proof of the Hartman-Wintner Law of the Iterated Logarithm. Ann. Probab. 11 (1983), no. 2, 270--276. doi:10.1214/aop/1176993596. https://projecteuclid.org/euclid.aop/1176993596


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