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Random Operators and Stochastic Equations

Editor-in-Chief: Girko, Vyacheslav

Managing Editor: Molchanov, S.

Editorial Board Member: Accardi, L. / Albeverio, Sergio / Carmona, R. / Casati, G. / Christopeit, N. / Domanski, C. / Drygas, Hilmar / Gupta, A.K. / Ibragimov, I. / Kirsch, Werner / Klein, A. / Kondratyev, Yuri / Kurotschka, V. / Leonenko, N. / Loubaton, Philippe / Orsingher, E. / Pastur, L. / Rodrigues, Waldyr A. / Shiryaev, Albert / Turbin, A.F. / Veretennikov, Alexandre

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Extrapolation of multidimensional stationary processes

Mikhail P. Moklyachuk / Aleksandr Yu. Masyutka

1Department of Probability Theory and Mathematical Statistics, Kyiv National University, Kyiv, 01033, Ukraine

2e-mail:

Citation Information: Random Operators and Stochastic Equations rose. Volume 14, Issue 3, Pages 233–244, ISSN (Online) 1569-397x, ISSN (Print) 0926-6364, DOI: 10.1515/156939706778239819, August 2006

Estimation problems are considered for a functional which depends on the unknown values of a multidimensional stationary stochastic process based on observations of the process for t < 0. Formulas are proposed for calculation the mean square error and the spectral characteristics of the optimal estimate of the functional under the condition that the spectral density of the process is known. The least favorable spectral densities and the minimax spectral characteristics of the optimal estimate of the functional are found for concrete classes of spectral densities.

Key Words: multidimensional stationary process,; optimal linear estimate,; mean square error,; spectral characteristics,; least favorable spectral density,; minimax-robust spectral characteristics.

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