Some generalizations of limit theorems of theory of probability
Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 4, pp. 729-734
Voir la notice de l'article provenant de la source Math-Net.Ru
Let $\xi_1,\dots,\xi_n,\dots$ be a sequence of independent random variables with non-monotonic distribution functions $V_1(x),\dots,V_n(x),\dots$ belonging to the class $В$ (i.e. $V_i(x)$ satisfy the condition (1.3)). The paper contains some results on convergence of distribution functions of sums
$$
s_n=\frac{\xi_1+\dots+\xi_n}{B_n}
$$
In to the functions $\Phi_{2q}(x)$ having “densities”
$$
\varphi_{2q}(x)=\frac1{\sqrt{2\pi}}\int_{-\infty}^\infty e^{-itx-\frac{t^{2q}}{(2q)}}\,dt.
$$
@article{TVP_1967_12_4_a11,
author = {Yu. P. Studnev},
title = {Some generalizations of limit theorems of theory of probability},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {729--734},
publisher = {mathdoc},
volume = {12},
number = {4},
year = {1967},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1967_12_4_a11/}
}
Yu. P. Studnev. Some generalizations of limit theorems of theory of probability. Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 4, pp. 729-734. http://geodesic.mathdoc.fr/item/TVP_1967_12_4_a11/