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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