Geodesic
The central limit theorem for the sums of functions of mixing sequences
Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 3, pp. 553-564 
V. T. Dubrovin; D. A. Moskvin. The central limit theorem for the sums of functions of mixing sequences. Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 3, pp. 553-564. http://geodesic.mathdoc.fr/item/TVP_1979_24_3_a8/
@article{TVP_1979_24_3_a8,
     author = {V. T. Dubrovin and D. A. Moskvin},
     title = {The central limit theorem for the sums of functions of mixing sequences},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {553--564},
     year = {1979},
     volume = {24},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1979_24_3_a8/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $a_1,a_2,\dots$ be a strictly stationary sequence of random variables, $f(x_1,\dots,x_s)$ be a measurable function and $$ \xi_{ks}=f(a_k,\dots,a_{k+s-1}),\qquad k=1,2,\dots $$ We prove that the central limit theorem holds for $\xi_{ks}$ with the remainder term $O(n^{2\omega^{-1/8}-1/2})$ if the sequence $\{a_k\}$ satisfies Rosenblatt's mixing condition with coefficient $\alpha(k)\le Ak^{-\omega}$ ($A>0$, $\omega>3996$) and for $s=s(n)$, $1\le s(n)\le \ln^2n$, the random variables $\xi_{ks}$ are uniformly bounded with probability 1 and $\mathbf E\xi_{ks}=0$.