Minimax filtration of linear transformations of stationary consequences

Abstract

We will consider the problem of determining a linear, mean-square optimal estimate of the transformation $A\xi = \sum_{j=0}^{\infty}a(j)\xi(-j)$  of a stationary random sequence $\xi(k)$ with density $f (\lambda)$ from observations of the sequence $\xi(k)+\eta(k)$ with $k\leq 0$, where $\eta(k)$ is a stationary sequence not correlated with $\xi (k)$ with density $g(\lambda)$. The least favorable spectral densities $f_0(\lambda)\in D_f$, $g_0(\lambda)\in D_g$, and minimax (robust) spectral characteristics of an optimal estimate $A\xi$ for different classes of densities $D_f$, $D_g$.