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The problem of the mean-square optimal linear estimation of the functional$A\xi=\ \int\limits_{R^s}a(t)\xi(-t)dt,$ which depends on the unknown values ofstochastic stationary process $\xi(t)$ from observations of the process$\xi(t)+\eta(t)$ at points $t\in\mathbb{R} ^{-} \backslash S $,$S=\bigcup\limits_{l=1}^{s}[-M_{l}-N_{l}, \, \ldots, \, -M_{l} ],$$R^s=[0,\infty) \backslash S^{+},$ $S^{+}=\bigcup\limits_{l=1}^{s}[ M_{l}, \,\ldots, \, M_{l}+N_{l}]$ is considered. Formulas for calculating themean-square error and the spectral characteristic of the optimal linearestimate of the functional are proposed under the condition of spectralcertainty, where spectral densities of the processes $\xi(t)$ and $\eta(t)$ areexactly known. The minimax (robust) method of estimation is applied in the casewhere spectral densities are not known exactly, but sets of admissible spectraldensities are given. Formulas that determine the least favorable spectraldensities and minimax spectral characteristics are proposed for some specialsets of admissible densities.

Filtering Problem for Functionals of Stationary Processes with Missing Observations