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
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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 $\varliminf\limits_{n\to\infty}n\delta_n>0$.
@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},
publisher = {mathdoc},
volume = {13},
number = {4},
year = {1968},
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 PB - mathdoc 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 %I mathdoc %U http://geodesic.mathdoc.fr/item/TVP_1968_13_4_a16/ %G ru %F TVP_1968_13_4_a16
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/