Geodesic
Asymptotic Representation for the~Distributions of Sums of Weakly Dependent Variables
Matematičeskie trudy, Tome 2 (1999) no. 2, pp. 21-56.

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In the present article, we study the asymptotic behavior of the distributions of sums of random variables from stationary sequences satisfying mixing conditions. We obtain a decomposition of the sums into the pairs of asymptotically independent components and deduce some well-known results in this field from the main theorems. 
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     author = {S. A. Klokov},
     title = {Asymptotic {Representation} for {the~Distributions} of {Sums} of {Weakly} {Dependent} {Variables}},
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S. A. Klokov. Asymptotic Representation for the~Distributions of Sums of Weakly Dependent Variables. Matematičeskie trudy, Tome 2 (1999) no. 2, pp. 21-56. http://geodesic.mathdoc.fr/item/MT_1999_2_2_a2/