Geodesic
Convergence of convolutions of concentration functions to degenerate, normal, and Poisson laws
Teoriâ veroâtnostej i ee primeneniâ, Tome 39 (1994) no. 2, pp. 248-271

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper compares the behavior of convolutions of distribution functions and that of convolutions of corresponding concentration functions. It is shown that the weak convergence of a sequence of convolutions of distribution functions is equivalent to the weak convergence of a sequence of convolutions of corresponding concentration functions to normal, Poisson, and degenerate laws. The most of statements are supposed to be uniform, inside the convolution, closeness of the concentration components to degenerate laws.
Keywords: concentration function, distribution function, weak convergence, random variable. 
@article{TVP_1994_39_2_a1,
     author = {Sh. O. Alekperov and V. M. Kruglov},
     title = {Convergence of convolutions of concentration functions to degenerate, normal, and {Poisson} laws},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {248--271},
     publisher = {mathdoc},
     volume = {39},
     number = {2},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1994_39_2_a1/}
}
TY  - JOUR
AU  - Sh. O. Alekperov
AU  - V. M. Kruglov
TI  - Convergence of convolutions of concentration functions to degenerate, normal, and Poisson laws
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 1994
SP  - 248
EP  - 271
VL  - 39
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_1994_39_2_a1/
LA  - ru
ID  - TVP_1994_39_2_a1
ER  - 
%0 Journal Article
%A Sh. O. Alekperov
%A V. M. Kruglov
%T Convergence of convolutions of concentration functions to degenerate, normal, and Poisson laws
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1994
%P 248-271
%V 39
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_1994_39_2_a1/
%G ru
%F TVP_1994_39_2_a1
Sh. O. Alekperov; V. M. Kruglov. Convergence of convolutions of concentration functions to degenerate, normal, and Poisson laws. Teoriâ veroâtnostej i ee primeneniâ, Tome 39 (1994) no. 2, pp. 248-271. http://geodesic.mathdoc.fr/item/TVP_1994_39_2_a1/