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.


60G35 Signal detection and filtering (aspects of stochastic processes)
60G15 Gaussian processes
93E10 Estimation and detection in stochastic control theory