Geodesic
On the limit distribution of sums of real random variables
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 10 (2017) no. 3, pp. 310-313

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

Considers centered sequence of absolutely continuous random variables with a non-trivial weak limit of the sums $\displaystyle \frac{1}{\sqrt{n}}\sum \limits_{i=1}^n\xi_i$. We found a general view of the limit distribution. It is shown that the form of the limit distribution depends only on the average mixed moments of the first order, describing the sequence of Rademacher random variables, into which can be decomposed the elements of the given sequence.
Keywords: dependent random variables, the sums of dependent random variables, limit distribution of sums of random variables, the normality of the limit distribution of sums of random variables. 
@article{JSFU_2017_10_3_a6,
     author = {Sergey V. Chebotarev},
     title = {On the limit distribution of sums of real random variables},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {310--313},
     publisher = {mathdoc},
     volume = {10},
     number = {3},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2017_10_3_a6/}
}
TY  - JOUR
AU  - Sergey V. Chebotarev
TI  - On the limit distribution of sums of real random variables
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2017
SP  - 310
EP  - 313
VL  - 10
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2017_10_3_a6/
LA  - en
ID  - JSFU_2017_10_3_a6
ER  - 
%0 Journal Article
%A Sergey V. Chebotarev
%T On the limit distribution of sums of real random variables
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2017
%P 310-313
%V 10
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2017_10_3_a6/
%G en
%F JSFU_2017_10_3_a6
Sergey V. Chebotarev. On the limit distribution of sums of real random variables. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 10 (2017) no. 3, pp. 310-313. http://geodesic.mathdoc.fr/item/JSFU_2017_10_3_a6/