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INTERPOLATION PROBLEMS FOR RANDOM FIELDS FROM OBSERVATIONS IN PERFORATED PLANE

unpublished

The problem of estimation of linear functionals which depend on the unknown values of a homogeneous random field g(k , j) in the region K c Z 2 from observations of the sum £(k, j) + ^ (k , j) at points (k , j) e Z 2 \ K is investigated. Formulas for calculating the mean square errors and the spectral characteristics of the opti mal linear estimate of functionals are derived in the case where the spectral densities are exactly known. Formulas that determine the least favourable spectral

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