Distribution of Symmetric Stable Laws of Index $2^{-n}$
Mitra, Shashanka S.
Ann. Probab., Tome 9 (1981) no. 6, p. 710-711 / Harvested from Project Euclid
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Let $X_1, X_2 \cdots, X_n(n \geq 2)$ be independent standard normal. Then the random variable $U = X_1/V_n$ where $V_n = \exp_2\lbrack 2^{n - 2} - 1\rbrack X_2(X_3)^2 \cdots(X^2_n)^{2^{n - 3}} \quad n \geq 3 \\ = X_2 \text{for} n = 2$ has a symmetric stable distribution with index $2^{2 - n}$.
Publié le : 1981-08-14
Classification:  Symmetric stable laws,  60E07 
@article{1176994380,
     author = {Mitra, Shashanka S.},
     title = {Distribution of Symmetric Stable Laws of Index $2^{-n}$},
     journal = {Ann. Probab.},
     volume = {9},
     number = {6},
     year = {1981},
     pages = { 710-711},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176994380}
}

Mitra, Shashanka S. Distribution of Symmetric Stable Laws of Index $2^{-n}$. Ann. Probab., Tome 9 (1981) no. 6, pp.  710-711. http://gdmltest.u-ga.fr/item/1176994380/