Open Access
October, 1991 Probability Laws with 1-Stable Marginals are 1-Stable
Gennady Samorodnitsky, Murad S. Taqqu
Ann. Probab. 19(4): 1777-1780 (October, 1991). DOI: 10.1214/aop/1176990235


We show that if $\mathbf{X} = (X_1,\ldots,X_d)$ is a vector in $\mathbb{R}^d$ and all linear combinations $\sum^d_{i=1}C_iX_i$ are 1-stable random variables, then $\mathbf{X}$ is itself 1-stable. More generally, a probability measure $\mu$ on a vector space whose univariate marginals are 1-stable is itself 1-stable. This settles an outstanding problem of Dudley and Kanter.


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Gennady Samorodnitsky. Murad S. Taqqu. "Probability Laws with 1-Stable Marginals are 1-Stable." Ann. Probab. 19 (4) 1777 - 1780, October, 1991.


Published: October, 1991
First available in Project Euclid: 19 April 2007

zbMATH: 0745.60013
MathSciNet: MR1127727
Digital Object Identifier: 10.1214/aop/1176990235

Primary: 60E07

Keywords: stable marginals , Stable measure , weak convergence

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.19 • No. 4 • October, 1991
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