Linear minimax filtering of a stationary random process under conditions of partial a priori uncertainty with respect to spectral density

A minimax statement of the problem of linear filtering is considered for the case of a stationary, in a broad sense, random process (useful signal) observed in an additive mixture with white noise. The spectral density of the useful signal is only known to satisfy the specified system of moment conditions and to be concentrated on a certain measurable space of the frequency axis. The saddle point of the resultant antagonistic game is found by solving a system of relations. An example is provided.