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Teoriya Veroyatnostei i ee Primeneniya, 1975, Volume 20, Issue 3, Pages 653–656
(Mi tvp3320)
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This article is cited in 4 scientific papers (total in 4 papers)
Short Communications
On generalized Poisson distribution on groups
G. M. Feldman Kharkov
Abstract:
The paper deals with the arithmetic of distributions on groups. Let $X$ be a locally compact Abelian separable metric group, $e(F)=e^{-F(X)}\biggl(E_0+F+\frac{F^{*2}}{2!}+\dots\biggl)$ is the generalized Poisson distribution associated with a finite measure $F$, and $I_0$ is a class of distributions without indecomposable or idempotent divisors. Some results are obtained on the conditions for generalized Poisson distributions to belong or not to belong to the class $I_0$. The density (in the weak topology) of the class $I_0$ in the set of all infinitely divisible distributions is also studied. If there is an element of the infinite order in any neighbourhood of zero in the group $X$, then the class $I_0$ is shown to be dense in the set of all infinitely divisible distributions. It is also proved that for discrete groups the density takes place if and only if $X\approx Z_2$.
Received: 27.05.1974
Citation:
G. M. Feldman, “On generalized Poisson distribution on groups”, Teor. Veroyatnost. i Primenen., 20:3 (1975), 653–656; Theory Probab. Appl., 20:3 (1976), 641–644
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