Teoriâ veroâtnostej i ee primeneniâ, Tome 26 (1981) no. 3, pp. 612-618
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G. M. Fel'dman; A. E. Fryntov. On decomposition of a convolution of two Poisson distributions on locally compact Abelian groups. Teoriâ veroâtnostej i ee primeneniâ, Tome 26 (1981) no. 3, pp. 612-618. http://geodesic.mathdoc.fr/item/TVP_1981_26_3_a15/
@article{TVP_1981_26_3_a15,
author = {G. M. Fel'dman and A. E. Fryntov},
title = {On decomposition of a~convolution of two {Poisson} distributions on locally compact {Abelian} groups},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {612--618},
year = {1981},
volume = {26},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1981_26_3_a15/}
}
TY - JOUR
AU - G. M. Fel'dman
AU - A. E. Fryntov
TI - On decomposition of a convolution of two Poisson distributions on locally compact Abelian groups
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1981
SP - 612
EP - 618
VL - 26
IS - 3
UR - http://geodesic.mathdoc.fr/item/TVP_1981_26_3_a15/
LA - ru
ID - TVP_1981_26_3_a15
ER -
%0 Journal Article
%A G. M. Fel'dman
%A A. E. Fryntov
%T On decomposition of a convolution of two Poisson distributions on locally compact Abelian groups
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1981
%P 612-618
%V 26
%N 3
%U http://geodesic.mathdoc.fr/item/TVP_1981_26_3_a15/
%G ru
%F TVP_1981_26_3_a15
Let $X$ be a locally compact Abelian separable group, $\displaystyle\pi=\operatorname{exp}\{-F(x)\}\sum_{n=0}^{\infty}F^{\ast n/n!}$ be the Poisson distribution (P. d.) on $X$ generated by the positive measure $F$ concentrated in the point $x\in X$. It is shown in the paper that if the elements $x_1$ and $x_2$ generating P. d.'s $\pi_1$ and $\pi_2$ have infinite order, then every divisor of the convolution $\mu=\pi_1\ast\pi_2$ is a shift of the convolution of two P. d.'s.
