On minimax filtration of vector processes

We study the problem of optimal linear estimation of the transformation of a stationary random process (t) with values in a Hilbert space by observations of the process (t) + (t) fort0. We obtain relations for computing the error and the spectral characteristic of the optimal linear estimate of the transformationA for given spectral densities of the processes (t) and (t). The minimax spectral characteristics and the least favorable spectral densities are obtained for various classes of densities.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 3, pp. 389–397, March, 1993.