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 
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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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