On extrapolation of transformations of random processes disturbed by the white noise

• Date: 2025
• Main Authors: Moklyachuk , M. P., Моклячук , М. П.
• Format: Article
• Language: Russian
• Published: Institute of Mathematics, NAS of Ukraine 2025
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/9360
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...