Geodesic
On a~Theorem of V.\,М.~Zolotarev
Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 1, pp. 96-99

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Let $\xi=\eta=\zeta$, where $\eta$ and $\zeta$ are independent random variables, $\eta$ has the probability density (7) and ${\mathbf E}\exp({\zeta/2})=K\infty$. It is shown that formula (10) is true if $m\geqq 1$, or if $0$ and condition (11) which is implied by (12) is satisfied. If ${\mathbf P}\{{\zeta0}\}=0$, inequality (13) holds for $m\geqq 1$. Formula (14) is true if conditions (15) and (in the case $r>m-1$) (16) are satisfied. An application to the random variable (1), a weighted sum of independent $\chi^2$ random variables, implies a result of V. M. Zolotarev [1]. 
@article{TVP_1964_9_1_a7,
     author = {Wassily Hoeffding},
     title = {On {a~Theorem} of {V.\,{\CYRM}.~Zolotarev}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {96--99},
     publisher = {mathdoc},
     volume = {9},
     number = {1},
     year = {1964},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1964_9_1_a7/}
}
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Wassily Hoeffding. On a~Theorem of V.\,М.~Zolotarev. Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 1, pp. 96-99. http://geodesic.mathdoc.fr/item/TVP_1964_9_1_a7/