A general solution of a problem in linear prediction of stationary processes

Let $\xi(t)$ and $\eta(t)$ be stationary in the wide sense processes, $\xi$ and $\eta$ being stationary connected. It is required to find the best linear prediction of a random variable $\xi(\tau)$, $\tau>0$, in terms of known values of $\xi(t)$ for $t\le0$ and $\eta(t)$ for $t\ge T$. In the paper a general solution of this problem is given.