Matematičeskie zametki, Tome 16 (1974) no. 5, pp. 777-782
Citer cet article
V. M. Kruglov. Characterization of a class of infinitely divisible distributions in Hilbert space. Matematičeskie zametki, Tome 16 (1974) no. 5, pp. 777-782. http://geodesic.mathdoc.fr/item/MZM_1974_16_5_a11/
@article{MZM_1974_16_5_a11,
author = {V. M. Kruglov},
title = {Characterization of a~class of infinitely divisible distributions in {Hilbert} space},
journal = {Matemati\v{c}eskie zametki},
pages = {777--782},
year = {1974},
volume = {16},
number = {5},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1974_16_5_a11/}
}
TY - JOUR
AU - V. M. Kruglov
TI - Characterization of a class of infinitely divisible distributions in Hilbert space
JO - Matematičeskie zametki
PY - 1974
SP - 777
EP - 782
VL - 16
IS - 5
UR - http://geodesic.mathdoc.fr/item/MZM_1974_16_5_a11/
LA - ru
ID - MZM_1974_16_5_a11
ER -
%0 Journal Article
%A V. M. Kruglov
%T Characterization of a class of infinitely divisible distributions in Hilbert space
%J Matematičeskie zametki
%D 1974
%P 777-782
%V 16
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_1974_16_5_a11/
%G ru
%F MZM_1974_16_5_a11
It is established that the spectral measure of an infinitely divisible distribution $F$ in a Hilbert space $H$ is concentrated in a sphere of finite radius if and only if the integral $\int_H\exp(\alpha\|x\|\ln(\|x\|+1))\,dF$ is finite for some number $\alpha>0$. If this integral is finite for any $\alpha>0$ then the infinitely divisible distribution $F$ is normal (maybe, degenerate).
