Geodesic
On the asymptotic normality of some sums of dependent random variables
Diskretnaya Matematika, Tome 27 (2015) no. 4, pp. 141-149

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

A theorem on the asymptotic normality of the sum of dependent random variables is stated and proved. Conditions of the theorem are formulated in terms of a dependency graph which characterizes the relationships between random variables. This theorem is used to prove the asymptotic normality of the sum of functions defined on subsets of elements of the stationary sequence satisfying the strong mixing condition. As an illustration of possible applications of these theorems we give a theorem on the asymptotic normality of the number of empty cells if the random sequence of cells occupied by particles is a stationary sequence satisfying the uniform strong mixing condition.
Keywords: sums of dependent variables, asymptotic normality, dependency graph, strong mixing condition. 
@article{DM_2015_27_4_a10,
     author = {M. I. Tikhomirova and V. P. Chistyakov},
     title = {On the asymptotic normality of some sums of dependent random variables},
     journal = {Diskretnaya Matematika},
     pages = {141--149},
     publisher = {mathdoc},
     volume = {27},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2015_27_4_a10/}
}
TY  - JOUR
AU  - M. I. Tikhomirova
AU  - V. P. Chistyakov
TI  - On the asymptotic normality of some sums of dependent random variables
JO  - Diskretnaya Matematika
PY  - 2015
SP  - 141
EP  - 149
VL  - 27
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2015_27_4_a10/
LA  - ru
ID  - DM_2015_27_4_a10
ER  - 
%0 Journal Article
%A M. I. Tikhomirova
%A V. P. Chistyakov
%T On the asymptotic normality of some sums of dependent random variables
%J Diskretnaya Matematika
%D 2015
%P 141-149
%V 27
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2015_27_4_a10/
%G ru
%F DM_2015_27_4_a10
M. I. Tikhomirova; V. P. Chistyakov. On the asymptotic normality of some sums of dependent random variables. Diskretnaya Matematika, Tome 27 (2015) no. 4, pp. 141-149. http://geodesic.mathdoc.fr/item/DM_2015_27_4_a10/