Geodesic
Enlargement of the Class of Geometrically Infinitely Divisible Random Variables
Publications de l'Institut Mathématique, _N_S_54 (1993) no. 68, p. 126 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

The class of negative binomial infinitely divisible random variables is introduced in the following way: Random variable $Y$ is called {\it negative binomial infinitely divisible\/} if there exist i.i.d. random variables $X^{(1)}_p,X^{(2)}_p,\dots$, $p\in(0,1)$, independent of $Y$ and $\nu^{(r)}_p$ and such that $ Y \mathrel{\mathop=^{\text {\rm d}}} łim_{p\to 0} \sum^{\nu_p^{(r)}}_{j=1} X^{(j)}_p, $ where $\nu^{(r)}_p$ has negative binomial law. \par The representation of characteristic functions from the class of negative binomial infinitely divisible random variables is given and also some related properties discussed. When $r=1$ the above class reduces to the well known class of geometrically infinitely divisible random variables.
Classification : 60E07 
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     author = {Slobodanka Jankovi\'c},
     title = {Enlargement of the {Class} of {Geometrically} {Infinitely} {Divisible} {Random} {Variables}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {126 },
     publisher = {mathdoc},
     volume = {_N_S_54},
     number = {68},
     year = {1993},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1993_N_S_54_68_a15/}
}
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Slobodanka Janković. Enlargement of the Class of Geometrically Infinitely Divisible Random Variables. Publications de l'Institut Mathématique, _N_S_54 (1993) no. 68, p. 126 . http://geodesic.mathdoc.fr/item/PIM_1993_N_S_54_68_a15/