On extrapolation of transformations of random processes disturbed by the white noise - Moklyachuk , M. P. (Ukrains’kyi Matematychnyi Zhurnal, 2025)
We consider the problem of linear mean square optimal estimation of transformation$Aξ = \int_0^{∞}a(t)ξ (t) dt$ of a stationary random process $ξ (t)$ in observations of process $ξ (t)+η(t)$ for $t≤ 0$, where $η (t)$ is white noise uncorrelated with $ξ (t)$. We find least favorable spectral densities $f_0(λ)\bar{\in} \mathcal{D}$ and minimax (robust) spectral characteristics of an optimal estimator of transformation $Aξ$ for various classes $\mathcal{D}$ of densities.