Geodesic
Central limit theorem for the Banach-valued weakly dependent random variables
Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 1, pp. 83-97

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Let $B$ be a separable Banach space, $\xi_i$ – a stationary sequence of $B$-valued random variables with zero mean. In this paper we investigate some conditions on the character and rate of mixing under which the sequence $\xi_i$ satisfies the central limit theorem, i. e. the sequence $$ S_n=n^{-1/2}(\xi_1+\dots+\xi_n),\qquad n\to\infty, $$ converges weakly to some Gaussian $B$-valued variable. 
@article{TVP_1983_28_1_a4,
     author = {V. A. Dmitrovskiǐ and S. V. Ermakov and E. I. Ostrovskiǐ},
     title = {Central limit theorem for the {Banach-valued} weakly dependent random variables},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {83--97},
     publisher = {mathdoc},
     volume = {28},
     number = {1},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1983_28_1_a4/}
}
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V. A. Dmitrovskiǐ; S. V. Ermakov; E. I. Ostrovskiǐ. Central limit theorem for the Banach-valued weakly dependent random variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 1, pp. 83-97. http://geodesic.mathdoc.fr/item/TVP_1983_28_1_a4/