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Teoriya Veroyatnostei i ee Primeneniya, 1968, Volume 13, Issue 4, Pages 742–745
(Mi tvp932)
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Short Communications
О некоторых свойствах сопровождающих законов для симметричных функций распределений
Yu. P. Studnev Uzhgorod
Abstract:
Let $\{\xi_k\}$ be a sequence of independent random variables with the same symmetric distribution function $F(x)$ which has a non-negative characteristic function and $F_n(x)$ be the distribution function of the sum $s_n=\xi_1+\dots+\xi_n$. Denote by $\mathfrak G$ the set of infinitely divisible laws.
In the paper we show by elementary methods that there exist such metrics
$$
\rho_i(F_n,G)\quad(G\in\mathfrak G),\quad i=1,2,\dots,
$$
invariant with respect, to linear transformations of the arguments, that the inequality
$$
\inf_{G\in\mathfrak G}\rho_i(F_n,G)\le Cn^{-1}
$$
where $C$ is an absolute constant, holds.
Received: 14.06.1966
Citation:
Yu. P. Studnev, “О некоторых свойствах сопровождающих законов для симметричных функций распределений”, Teor. Veroyatnost. i Primenen., 13:4 (1968), 742–745; Theory Probab. Appl., 13:4 (1968), 701–703
Linking options:
https://www.mathnet.ru/eng/tvp932 https://www.mathnet.ru/eng/tvp/v13/i4/p742
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Abstract page: | 198 | Full-text PDF : | 72 |
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