On minimax filtration of vector processes - Moklyachuk, M. P. (Ukrains’kyi Matematychnyi Zhurnal, 1993)
We study the problem of optimal linear estimation of the transformation $Aξ = \smallint _0^∞< a(t), ξ ( - t) > dt$ 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.