## The Annals of Probability

- Ann. Probab.
- Volume 22, Number 1 (1994), 1-16.

### Stable Limits for Associated Random Variables

Andre Robert Dabrowski and Adam Jakubowski

#### Abstract

We consider a stationary sequence of associated real random variables and state conditions which guarantee that partial sums of this sequence, when properly normalized, converge in distribution to a stable, non-Gaussian limit. Limit theorems for jointly stable and associated random variables are investigated in detail. In the general case we assume that finite-dimensional distributions belong to the domain of attraction of multidimensional strictly stable laws and that there is a bound on the positive dependence given by finiteness of an analog to the lag covariance series.

#### Article information

**Source**

Ann. Probab., Volume 22, Number 1 (1994), 1-16.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176988845

**Digital Object Identifier**

doi:10.1214/aop/1176988845

**Mathematical Reviews number (MathSciNet)**

MR1258863

**Zentralblatt MATH identifier**

0793.60018

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60F05: Central limit and other weak theorems

Secondary: 60E07: Infinitely divisible distributions; stable distributions

**Keywords**

Central limit theorem $\alpha$-stable association

#### Citation

Dabrowski, Andre Robert; Jakubowski, Adam. Stable Limits for Associated Random Variables. Ann. Probab. 22 (1994), no. 1, 1--16. doi:10.1214/aop/1176988845. https://projecteuclid.org/euclid.aop/1176988845