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Conditionally optimal interpolation of random sequences defined by difference equations. (English. Russian original) Zbl 0828.60027
Russ. Acad. Sci., Dokl., Math. 49, No. 3, 539-544 (1994); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 336, No. 4, 453-456 (1994).
Summary: We present a development of the theory of conditionally optimal filtering and extrapolation by the mean square criterion [see V. S. Pugachev, Soviet Math., Dokl. 19, 1495-1497 (1978), translation from Dokl. Akad. Nauk SSSR 243, 1131-1134 (1978; Zbl 0421.93063); ibid. 25, 79-82 (1982), resp. ibid. 262, 535-538 (1982; Zbl 0496.60052); and “Probability theory and mathematical statistics” (1984; Zbl 0533.60001)] to problems of interpolation of random sequences defined by nonlinear difference equations. The interpolations obtained on the basis of our theory may be used in real-time observation processing in many problems of statistical information science and control, where, to find a more complete information about the process being observed, it is necessary to take into account observations at a later time.

60G25 Prediction theory (aspects of stochastic processes)
60G35 Signal detection and filtering (aspects of stochastic processes)