## The Annals of Probability

### A Stable Local Limit Theorem

J. Mineka

#### 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

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