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Teoriya Veroyatnostei i ee Primeneniya, 1968, Volume 13, Issue 4, Pages 742–745 (Mi tvp932)  

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
English version:
Theory of Probability and its Applications, 1968, Volume 13, Issue 4, Pages 701–703
DOI: https://doi.org/10.1137/1113088
Bibliographic databases:
Document Type: Article
Language: Russian
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
Citation in format AMSBIB
\Bibitem{Stu68}
\by Yu.~P.~Studnev
\paper О некоторых свойствах сопровождающих законов для симметричных функций распределений
\jour Teor. Veroyatnost. i Primenen.
\yr 1968
\vol 13
\issue 4
\pages 742--745
\mathnet{http://mi.mathnet.ru/tvp932}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=242220}
\zmath{https://zbmath.org/?q=an:0177.46104|0169.49601}
\transl
\jour Theory Probab. Appl.
\yr 1968
\vol 13
\issue 4
\pages 701--703
\crossref{https://doi.org/10.1137/1113088}
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