The Annals of Probability

A Stable Local Limit Theorem

J. Mineka

Full-text: Open access

Abstract

Conditions are given which imply that the partial sums of a sequence of independent integer-valued random variables, suitably normalized, converge in distribution to a stable law of exponent $\alpha, 0 < \alpha < 2$, and imply as well that a strong version of the corresponding local limit theorem holds.

Article information

Source
Ann. Probab., Volume 2, Number 1 (1974), 167-172.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996764

Digital Object Identifier
doi:10.1214/aop/1176996764

Mathematical Reviews number (MathSciNet)
MR356182

Zentralblatt MATH identifier
0295.60036

JSTOR
links.jstor.org

Subjects
Primary: 60F99: None of the above, but in this section
Secondary: 60G50: Sums of independent random variables; random walks

Keywords
Stable local limit theorem sums of independent integer-valued random variables

Citation

Mineka, J. A Stable Local Limit Theorem. Ann. Probab. 2 (1974), no. 1, 167--172. doi:10.1214/aop/1176996764. https://projecteuclid.org/euclid.aop/1176996764


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