On extrapolation of transformations of random processes disturbed by the white noise

Abstract

We consider the problem of linear mean square optimal estimation of transformation

$A\xi = \int_0^{\infty}a(t)\xi (t) dt$ of a stationary random process $\xi (t)$  in observations of process $\xi (t)+\eta(t)$ for $t\leq 0$, where $\eta (t)$ is white noise uncorrelated with $\xi (t)$. We find least favorable spectral densities $f_0(\lambda)\bar{\in} \mathcal{D}$ and minimax (robust) spectral characteristics of an optimal estimator of transformation $A\xi$ for various classes $\mathcal{D}$ of densities.