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Minimax filtering of linear transforms of stationary processes. (English. Russian original) Zbl 0788.62084

Theory Probab. Math. Stat. 44, 95-102 (1992); translation from Teor. Veroyatn. Mat. Stat., Kiev 44, 96-105 (1991).
Summary: This article considers the problem of linear mean-square optimal estimation of the transform \(A\xi= \int^ \infty_ 0 a(t)\xi(-t)dt\) of a stationary random process \(\xi(t)\) with density \(f(\lambda)\) from observations of the process \(\xi(t)+ \eta(t)\) for \(t\leq 0\), where \(\eta(t)\) is a stationary random process with density \(g(\lambda)\) that is uncorrelated with \(\xi(t)\).
Formulas are obtained for computing the mean-square error and the spectral characteristic of an optimal linear estimator of the transform \(A\xi\). The least favorable spectral densities \(f_ 0(\lambda)\in{\mathcal D}_ f\) and \(g_ 0(\lambda)\in{\mathcal D}_ g\) and the minimax (robust) spectral characteristics of an optimal estimator of \(A\xi\) are found for various classes \({\mathcal D}_ f\) and \({\mathcal D}_ g\) of densities.

MSC:

62M20 Inference from stochastic processes and prediction
60G35 Signal detection and filtering (aspects of stochastic processes)
60G10 Stationary stochastic processes
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