The Annals of Probability

Stable Limits for Associated Random Variables

Andre Robert Dabrowski and Adam Jakubowski

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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


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