Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 4, pp. 712-724
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V. M. Zolotarev; V. M. Kruglov. The structure of infinitely divisible distributions on a bicompact Abelian group. Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 4, pp. 712-724. http://geodesic.mathdoc.fr/item/TVP_1975_20_4_a1/
@article{TVP_1975_20_4_a1,
author = {V. M. Zolotarev and V. M. Kruglov},
title = {The structure of infinitely divisible distributions on a~bicompact {Abelian} group},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {712--724},
year = {1975},
volume = {20},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1975_20_4_a1/}
}
TY - JOUR
AU - V. M. Zolotarev
AU - V. M. Kruglov
TI - The structure of infinitely divisible distributions on a bicompact Abelian group
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1975
SP - 712
EP - 724
VL - 20
IS - 4
UR - http://geodesic.mathdoc.fr/item/TVP_1975_20_4_a1/
LA - ru
ID - TVP_1975_20_4_a1
ER -
%0 Journal Article
%A V. M. Zolotarev
%A V. M. Kruglov
%T The structure of infinitely divisible distributions on a bicompact Abelian group
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1975
%P 712-724
%V 20
%N 4
%U http://geodesic.mathdoc.fr/item/TVP_1975_20_4_a1/
%G ru
%F TVP_1975_20_4_a1
Any probability distribution can be written in the form $$ F=\alpha_1F_1+\alpha_2F_2+\alpha_3F_3,\quad\alpha_j\ge0,\quad\alpha_1+\alpha_2+\alpha_3=1, $$ where $F_1$ is an absolutely continuous, $F_2$ a singular and $F_3$ a discrete probability distribution. We consider the following problem: what properties of the spectral measure of an infinitely divisible distribution $F$ involve $\alpha_j>0$ ($j=1,2,3$)?
