  We classify simple symmetries for an Ornstein-Uhlenbeck process, describing a
particle in an external force field $f(x)$. It turns out that for sufficiently
regular (in a sense to be defined) forces there are nontrivial symmetries only
if $f(x)$ is at most linear. We fully discuss the isotropic case, while for the
non-isotropic we only deal with a generic situation (defined in detail in the
text).
