## The Annals of Probability

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

### A Stable Local Limit Theorem

#### 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