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Teoriya Veroyatnostei i ee Primeneniya, 1981, Volume 26, Issue 3, Pages 612–618
(Mi tvp2619)
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This article is cited in 2 scientific papers (total in 2 papers)
Short Communications
On decomposition of a convolution of two Poisson distributions on locally compact Abelian groups
G. M. Fel'dman, A. E. Fryntov Har'kov
Abstract:
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.
Received: 18.08.1978
Citation:
G. M. Fel'dman, A. E. Fryntov, “On decomposition of a convolution of two Poisson distributions on locally compact Abelian groups”, Teor. Veroyatnost. i Primenen., 26:3 (1981), 612–618; Theory Probab. Appl., 26:3 (1982), 601–607
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