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On the Asymptotic Behaviour of the Prediction Error
Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 4, pp. 695-703 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $\{x_j\}$ be a stationary stochastic process in the wide sense which is regular, with spectral density function $f(\lambda)$. 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 $\delta_n=\sigma_n^2-\sigma_\infty^2=\sigma_n^2-\sigma^2$. The rate of convergence $\delta_n\downarrow 0$ is investigated in this article. 
@article{TVP_1964_9_4_a9,
     author = {I. A. Ibragimov},
     title = {On the {Asymptotic} {Behaviour} of the {Prediction} {Error}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {695--703},
     year = {1964},
     volume = {9},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1964_9_4_a9/}
}
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I. A. Ibragimov. On the Asymptotic Behaviour of the Prediction Error. Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 4, pp. 695-703. http://geodesic.mathdoc.fr/item/TVP_1964_9_4_a9/