Probability Laws with 1-Stable Marginals are 1-Stable
Samorodnitsky, Gennady ; Taqqu, Murad S.
Ann. Probab., Tome 19 (1991) no. 4, p. 1777-1780 / Harvested from Project Euclid
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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.
Publié le : 1991-10-14
Classification:  Stable measure,  stable marginals,  weak convergence,  60E07 
@article{1176990235,
     author = {Samorodnitsky, Gennady and Taqqu, Murad S.},
     title = {Probability Laws with 1-Stable Marginals are 1-Stable},
     journal = {Ann. Probab.},
     volume = {19},
     number = {4},
     year = {1991},
     pages = { 1777-1780},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176990235}
}

Samorodnitsky, Gennady; Taqqu, Murad S. Probability Laws with 1-Stable Marginals are 1-Stable. Ann. Probab., Tome 19 (1991) no. 4, pp.  1777-1780. http://gdmltest.u-ga.fr/item/1176990235/