On minimax filtration of vector processes
We study the problem of optimal linear estimation of the transformation $A\xi = \smallint _0^\infty< a(t), \xi ( - t) > dt$ of a stationary random process $ξ(t)$ with values in a Hilbert space by observations of the process $ξ(t) + η(t)$ for $t ⩽ 0$. We obtain relations for computin...
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| Datum: | 1993 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
1993
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5821 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | We study the problem of optimal linear estimation of the transformation $A\xi = \smallint _0^\infty< a(t), \xi ( - t) > dt$ of a stationary random process $ξ(t)$ with values in a Hilbert space by observations of the process $ξ(t) + η(t)$ for $t ⩽ 0$. We obtain relations for computing the error and the spectral characteristic of the optimal linear estimate of the transformation $Aξ$ for given spectral densities of the processes $ξ(t)$ and $η(t)$. The minimax spectral characteristics and the least favorable spectral densities are obtained for various classes of densities. |
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