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

Voir la notice de l'article provenant de la source Library of Science

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 
@article{DMPS_2007_27_1-2_a4,
     author = {Malinowski, Marek},
     title = {Geometrically strictly semistable laws as the limit laws},
     journal = {Discussiones Mathematicae. Probability and Statistics},
     pages = {79--97},
     publisher = {mathdoc},
     volume = {27},
     number = {1-2},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMPS_2007_27_1-2_a4/}
}
TY  - JOUR
AU  - Malinowski, Marek
TI  - Geometrically strictly semistable laws as the limit laws
JO  - Discussiones Mathematicae. Probability and Statistics
PY  - 2007
SP  - 79
EP  - 97
VL  - 27
IS  - 1-2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMPS_2007_27_1-2_a4/
LA  - en
ID  - DMPS_2007_27_1-2_a4
ER  - 
%0 Journal Article
%A Malinowski, Marek
%T Geometrically strictly semistable laws as the limit laws
%J Discussiones Mathematicae. Probability and Statistics
%D 2007
%P 79-97
%V 27
%N 1-2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMPS_2007_27_1-2_a4/
%G en
%F DMPS_2007_27_1-2_a4
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/