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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1975, Volume 20, Issue 3, Pages 653–656 (Mi tvp3320)

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, $e(F)=e^{-F(X)}(E_0+F+\frac{F^{*2}}{2!}+…)$ 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 $X\approx Z_2$.

Full text: PDF file (351 kB)

English version:
Theory of Probability and its Applications, 1976, 20:3, 641–644

Bibliographic databases:

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

Citation in format AMSBIB
\Bibitem{Fel75} \by G.~M.~Feldman \paper On generalized Poisson distribution on groups \jour Teor. Veroyatnost. i Primenen. \yr 1975 \vol 20 \issue 3 \pages 653--656 \mathnet{http://mi.mathnet.ru/tvp3320} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=378017} \zmath{https://zbmath.org/?q=an:0362.60027} \transl \jour Theory Probab. Appl. \yr 1976 \vol 20 \issue 3 \pages 641--644 \crossref{https://doi.org/10.1137/1120071}