Geodesic
Geometrically strictly semistable laws as the limit laws
Discussiones Mathematicae. Probability and Statistics, Tome 27 (2007) no. 1-2, pp. 79-97

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A random variable X is geometrically infinitely divisible iff for every p ∈ (0,1) there exists random variable X_p such that Xd= ∑_k=1^T(p)X_p,k, where X_p,k's are i.i.d. copies of X_p, and random variable T(p) independent of X_p,1,X_p,2,... has geometric distribution with the parameter p. In the paper we give some new characterization of geometrically infinitely divisible distribution. The main results concern geometrically strictly semistable distributions which form a subset of geometrically infinitely divisible distributions. We show that they are limit laws for random and deterministic sums of independent random variables.
Keywords: infinite divisibility, geometric infinite divisibility, geometric semistability, random sums, limit laws, characteristic function 
Malinowski, Marek. Geometrically strictly semistable laws as the limit laws. Discussiones Mathematicae. Probability and Statistics, Tome 27 (2007) no. 1-2, pp. 79-97. http://geodesic.mathdoc.fr/item/DMPS_2007_27_1-2_a4/
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