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).

• 34F05 - Ordinary differential equations and systems with randomness
• 35R60 - PDEs with randomness, stochastic partial differential equations
• 60H10 - Stochastic ordinary differential equations (aspects of stochastic analysis)
• 60H15 - Stochastic partial differential equations (aspects of stochastic analysis)