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.

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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. 
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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/

[1] S. V. Chebotarev, “On Limit Distribution of Sums of Random Variables”, Journal of Siberian Federal University. Mathematics $\$ Physics, 9:1 (2016), 17–29 | DOI

[2] S. V. Chebotarev, “About sequences of random variables with averaged links”, Vestnik AltSPA, seriya: estestv. i tochnye nauki, 7 (2011), 28–37 (in Russian)