Masyutka O. Estimation of functionals from multidimensional stationary processes under conditions of uncertainty

The considered problems are estimation of the functionals from multidimensional stationary sequences and multidimensional stationary processes under conditions of spectral certainty and spectral uncertainty. Formulas are obtained for calculation of the spectral characteristics and the mean square errors of optimal estimates of functionals for the extrapolation, filtration and interpolatioin problems. The problem of minimax extrapolation, filtration and interpolatioin of functionals is determined and solved for special classes of spectral uncertainty. The minimax spectral characteristics of optimal estimates of functionals and the maximal mean square errors are found.