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Teor. Veroyatnost. i Primenen., 1981, Volume 26, Issue 3, Pages 612–618 (Mi tvp2619)  

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.

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English version:
Theory of Probability and its Applications, 1982, 26:3, 601–607

Bibliographic databases:

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

Citation in format AMSBIB
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\by G.~M.~Fel'dman, A.~E.~Fryntov
\paper On decomposition of a~convolution of two Poisson distributions on locally compact Abelian groups
\jour Teor. Veroyatnost. i Primenen.
\yr 1981
\vol 26
\issue 3
\pages 612--618
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\zmath{https://zbmath.org/?q=an:0488.60016|0473.60011}
\transl
\jour Theory Probab. Appl.
\yr 1982
\vol 26
\issue 3
\pages 601--607
\crossref{https://doi.org/10.1137/1126067}
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