Central limit theorem for the Banach-valued weakly dependent random variables
Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 1, pp. 83-97
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},
year = {1983},
volume = {28},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1983_28_1_a4/}
}
TY - JOUR AU - V. A. Dmitrovskiǐ AU - S. V. Ermakov AU - E. I. Ostrovskiǐ TI - Central limit theorem for the Banach-valued weakly dependent random variables JO - Teoriâ veroâtnostej i ee primeneniâ PY - 1983 SP - 83 EP - 97 VL - 28 IS - 1 UR - http://geodesic.mathdoc.fr/item/TVP_1983_28_1_a4/ LA - ru ID - TVP_1983_28_1_a4 ER -
%0 Journal Article %A V. A. Dmitrovskiǐ %A S. V. Ermakov %A E. I. Ostrovskiǐ %T Central limit theorem for the Banach-valued weakly dependent random variables %J Teoriâ veroâtnostej i ee primeneniâ %D 1983 %P 83-97 %V 28 %N 1 %U http://geodesic.mathdoc.fr/item/TVP_1983_28_1_a4/ %G ru %F TVP_1983_28_1_a4
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/