On extrapolation of transformations of random processes disturbed by the white noise
We consider the problem of linear mean square optimal estimation of transformation $A\xi = \int_0^{\infty}a(t)\xi (t) dt$ of a stationary random process $\xi (t)$ in observations of process $\xi (t)+\eta(t)$ for $t\leq 0$, where $\eta (t)$ is white noise uncorrelated with $\xi (t)$. We find least f...
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| Date: | 2025 |
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| Language: | Russian |
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Institute of Mathematics, NAS of Ukraine
2025
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/9360 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513514404184064 |
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| author | Moklyachuk , M. P. Моклячук , М. П. |
| author_facet | Moklyachuk , M. P. Моклячук , М. П. |
| author_sort | Moklyachuk , M. P. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2025-06-30T14:20:55Z |
| description | We consider the problem of linear mean square optimal estimation of transformation
$A\xi = \int_0^{\infty}a(t)\xi (t) dt$ of a stationary random process $\xi (t)$ in observations of process $\xi (t)+\eta(t)$ for $t\leq 0$, where $\eta (t)$ is white noise uncorrelated with $\xi (t)$. We find least favorable spectral densities $f_0(\lambda)\bar{\in} \mathcal{D}$ and minimax (robust) spectral characteristics of an optimal estimator of transformation $A\xi$ for various classes $\mathcal{D}$ of densities. |
| first_indexed | 2026-03-24T03:45:53Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-9360 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus |
| last_indexed | 2026-03-24T03:45:53Z |
| publishDate | 2025 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/e0/8791fa4fdfc57f1b5d6ed075cc99f8e0.pdf |
| spelling | umjimathkievua-article-93602025-06-30T14:20:55Z On extrapolation of transformations of random processes disturbed by the white noise Об экстраполяции преобразований случайных процессов, возмущаемых белым шумом Moklyachuk , M. P. Моклячук , М. П. - We consider the problem of linear mean square optimal estimation of transformation $A\xi = \int_0^{\infty}a(t)\xi (t) dt$ of a stationary random process $\xi (t)$ in observations of process $\xi (t)+\eta(t)$ for $t\leq 0$, where $\eta (t)$ is white noise uncorrelated with $\xi (t)$. We find least favorable spectral densities $f_0(\lambda)\bar{\in} \mathcal{D}$ and minimax (robust) spectral characteristics of an optimal estimator of transformation $A\xi$ for various classes $\mathcal{D}$ of densities. Рассмотрена задача линейного среднеквадратически оптимального оценивания преобразования $A\xi = \int_0^{\infty}a(t)\xi (t) dt$ стационарного случайного процесса $\xi (t)$ по наблюдениям процесса $\xi (t)+\eta(t)$ при $t\leq 0$, где $\eta (t)$ — некоррелированный с $\xi (t)$ белый шум. Найдены наименее благоприятные спектральные плотности $f_0(\lambda)\bar{\in} \mathcal{D}$ и минимаксные (робастные) спектральные характеристики оптимальной оценки преобразования $A\xi$ для различных классов плотностей $\mathcal{D}$. Розглянута задача лінійного середньоквадратично оптимального оцінювання перетворення $A\xi = \int_0^{\infty}a(t)\xi (t) dt$ стаціонарного випадкового процесу $\xi (t)$ за спостереженнями процесу $\xi (t)+\eta(t)$ при $t\leq 0$, де $\eta (t)$ — некорельований з $\xi (t)$ білий шум. Знайдені найменш сприятливі спектральні щільності $f_0(\lambda)\bar{\in} \mathcal{D}$ та мінімаксні (робастні) спектральні характеристики оптимальної оцінки перетворення $A\xi$ для різних класів щільностей $\mathcal{D}$. Institute of Mathematics, NAS of Ukraine 2025-06-30 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/9360 Ukrains’kyi Matematychnyi Zhurnal; Vol. 43 No. 2 (1991); 216-223 Український математичний журнал; Том 43 № 2 (1991); 216-223 1027-3190 rus https://umj.imath.kiev.ua/index.php/umj/article/view/9360/10510 Copyright (c) 1991 М. П. Моклячук |
| spellingShingle | Moklyachuk , M. P. Моклячук , М. П. On extrapolation of transformations of random processes disturbed by the white noise |
| title | On extrapolation of transformations of random processes disturbed by the white noise |
| title_alt | Об экстраполяции преобразований случайных процессов, возмущаемых белым шумом |
| title_full | On extrapolation of transformations of random processes disturbed by the white noise |
| title_fullStr | On extrapolation of transformations of random processes disturbed by the white noise |
| title_full_unstemmed | On extrapolation of transformations of random processes disturbed by the white noise |
| title_short | On extrapolation of transformations of random processes disturbed by the white noise |
| title_sort | on extrapolation of transformations of random processes disturbed by the white noise |
| topic_facet | - |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9360 |
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