Open Access
January, 1994 Stable Limits for Associated Random Variables
Andre Robert Dabrowski, Adam Jakubowski
Ann. Probab. 22(1): 1-16 (January, 1994). DOI: 10.1214/aop/1176988845


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.


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Andre Robert Dabrowski. Adam Jakubowski. "Stable Limits for Associated Random Variables." Ann. Probab. 22 (1) 1 - 16, January, 1994.


Published: January, 1994
First available in Project Euclid: 19 April 2007

zbMATH: 0793.60018
MathSciNet: MR1258863
Digital Object Identifier: 10.1214/aop/1176988845

Primary: 60F05
Secondary: 60E07

Keywords: $\alpha$-stable , association , central limit theorem

Rights: Copyright © 1994 Institute of Mathematical Statistics

Vol.22 • No. 1 • January, 1994
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