Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 4, pp. 746-750
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I. A. Ibragimov; V. N. Solev. The asymptotic behavior of the prediction error of a stationary sequence with a spectral density of special type. Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 4, pp. 746-750. http://geodesic.mathdoc.fr/item/TVP_1968_13_4_a16/
@article{TVP_1968_13_4_a16,
author = {I. A. Ibragimov and V. N. Solev},
title = {The asymptotic behavior of the prediction error of a~stationary sequence with a~spectral density of special type},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {746--750},
year = {1968},
volume = {13},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1968_13_4_a16/}
}
TY - JOUR
AU - I. A. Ibragimov
AU - V. N. Solev
TI - The asymptotic behavior of the prediction error of a stationary sequence with a spectral density of special type
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1968
SP - 746
EP - 750
VL - 13
IS - 4
UR - http://geodesic.mathdoc.fr/item/TVP_1968_13_4_a16/
LA - ru
ID - TVP_1968_13_4_a16
ER -
%0 Journal Article
%A I. A. Ibragimov
%A V. N. Solev
%T The asymptotic behavior of the prediction error of a stationary sequence with a spectral density of special type
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1968
%P 746-750
%V 13
%N 4
%U http://geodesic.mathdoc.fr/item/TVP_1968_13_4_a16/
%G ru
%F TVP_1968_13_4_a16
Let $\{\xi_i\}$ be a stationary in the wide sense regular stochastic process with the spectral density function defined by (2). Denote by $\sigma_n^2$ the mean square prediction error in predicting $x_0$ by linear forms in $x_{-1},x_{-2},\dots,x_{-n}$. Let $\delta_n=\sigma_n^2-\sigma_\infty^2=\sigma_n^2-\sigma^2$, then $\delta_n=O(\frac1n)$ and $\varliminf\limits_{n\to\infty}n\delta_n>0$.
