The Annals of Probability

Note on a Limit Theorem

D. A. Darling

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Abstract

A simple derivation of a limiting distribution of Logan, Mallows, Rice and Shepp is found. This is the limiting distribution of a sequence of partial sums of independent, identically distributed random variables in the domain of attraction of a stable law, normalized by the partial sums of the absolute values of these variables.

Article information

Source
Ann. Probab., Volume 3, Number 5 (1975), 876-878.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996274

Digital Object Identifier
doi:10.1214/aop/1176996274

Mathematical Reviews number (MathSciNet)
MR436274

Zentralblatt MATH identifier
0313.60022

JSTOR
links.jstor.org

Subjects
Primary: 60G50: Sums of independent random variables; random walks

Keywords
60F0F Limit theorems stable distributions sums of independent random variables

Citation

Darling, D. A. Note on a Limit Theorem. Ann. Probab. 3 (1975), no. 5, 876--878. doi:10.1214/aop/1176996274. https://projecteuclid.org/euclid.aop/1176996274


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Corrections

  • See Correction: D. A. Darling. Note: Correction to "Note on a Limit Theorem". Ann. Probab., Vol. 4, Iss. 4 (1976), 697.