We have an OU process fulfilling the following SDE
$dx_t=A(t)x_tdt+S(t)\xi_tdt$,
where $\xi_t$ is a (Gaussian) white noise, $<\xi_t\xi_s>=\delta(t-s)$. What is the correlation between $x_t$ and $\xi_s$($<x_t\xi_s>=?$)?
For $t<s$ it is definitely zero, and for later times?