Geodesic
On the Stability of Solutions to Linear Problems for Stationary Processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 3, pp. 528-530 
Yu. A. Rozanov. On the Stability of Solutions to Linear Problems for Stationary Processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 3, pp. 528-530. http://geodesic.mathdoc.fr/item/TVP_1964_9_3_a9/
@article{TVP_1964_9_3_a9,
     author = {Yu. A. Rozanov},
     title = {On the {Stability} of {Solutions} to {Linear} {Problems} for {Stationary} {Processes}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {528--530},
     year = {1964},
     volume = {9},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1964_9_3_a9/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\xi(t)$ be a stationary process with spectral function $F(\lambda)$, prediction error $$ \sigma^2=\inf\int\left|e^{i\lambda\tau}-\sum_{t\in T}c(t)e^{i\lambda t}\right|^2dF(\lambda) $$ and let $$ \delta(G)^2=\inf\int\left|e^{i\lambda\tau}-\sum_{t\in T}c(t)e^{i\lambda t}\right|^2dF_1(\lambda), $$ where $F_1(\lambda)=F(\lambda)+G(\lambda)$, $dG(\lambda)\geqq 0$ and $\int{dG(\lambda)\leqq h^2}$. Then $\lim\limits_{h\to 0}\sup\limits_G\delta(G)=\sigma$. Other linear problems similar to the prediction one have solutions with the same properties.