The Annals of Probability

Rapidly Growing Random Walks and an Associated Stopping Time

Henry Teicher

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Abstract

An exponential limit distribution is obtained for stopping times associated with partial sums of independent, identically distributed random variables whose distribution function is slowly varying at infinity. It is also demonstrated that a generalized law of the iterated logarithm cannot obtain in such a case.

Article information

Source
Ann. Probab., Volume 7, Number 6 (1979), 1078-1081.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994903

Digital Object Identifier
doi:10.1214/aop/1176994903

Mathematical Reviews number (MathSciNet)
MR548904

Zentralblatt MATH identifier
0424.60024

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60F15: Strong theorems

Keywords
Random walk stopping time slowly varying generalized law of the iterated logarithm

Citation

Teicher, Henry. Rapidly Growing Random Walks and an Associated Stopping Time. Ann. Probab. 7 (1979), no. 6, 1078--1081. doi:10.1214/aop/1176994903. https://projecteuclid.org/euclid.aop/1176994903


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