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
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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.
@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},
publisher = {mathdoc},
volume = {26},
number = {3},
year = {1981},
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 PB - mathdoc 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 %I mathdoc %U http://geodesic.mathdoc.fr/item/TVP_1981_26_3_a15/ %G ru %F TVP_1981_26_3_a15
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/