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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| Дата: | 2025 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2025
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/9360 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | 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. |
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