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On the effectiveness in a problem of nonlinear prognosis and filtration. (Russian. English summary) Zbl 0553.60046
Let \(\zeta =\phi (\eta),\xi_ t=\phi_ t(\eta_ t)\), \(t\in T\), where \(\phi(\cdot)\), \(\phi_ t(\cdot)\in L_ 2(d\Phi)\) with the standard normal distribution \(\Phi\) and \(\eta\), \(\eta_ t\), \(t\in T\), is a Gaussian system of random variables with parameters in (0,1). The question of finding the best (in the mean square sense) linear and nonlinear estimations of a random variable \(\zeta\) (when the \(\eta_ t\), \(t\in T\), system is observed) and the character change of the \(\bar D/\tilde D\) relation are studied, where \(\bar D\) is the mean square error of linear estimation, and \(\tilde D\) is the mean square error of nonlinear estimation.
MSC:
60G35 Signal detection and filtering (aspects of stochastic processes)
60G15 Gaussian processes
93E10 Estimation and detection in stochastic control theory
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