О некоторых свойствах сопровождающих законов для симметричных функций распределений
Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 4, pp. 742-745
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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.
@article{TVP_1968_13_4_a15,
author = {Yu. P. Studnev},
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journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {742--745},
publisher = {mathdoc},
volume = {13},
number = {4},
year = {1968},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1968_13_4_a15/}
}
TY - JOUR AU - Yu. P. Studnev TI - О некоторых свойствах сопровождающих законов для симметричных функций распределений JO - Teoriâ veroâtnostej i ee primeneniâ PY - 1968 SP - 742 EP - 745 VL - 13 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TVP_1968_13_4_a15/ LA - ru ID - TVP_1968_13_4_a15 ER -
Yu. P. Studnev. О некоторых свойствах сопровождающих законов для симметричных функций распределений. Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 4, pp. 742-745. http://geodesic.mathdoc.fr/item/TVP_1968_13_4_a15/