  We consider a particle moving with equation of motion $\dot x=f(t)$, where
$f(t)$ is a random function with statistics which are independent of $x$ and
$t$, with a finite drift velocity $v=\langle f\rangle$ and in the presence of a
reflecting wall. Far away from the wall, translational invariance implies that
the stationary probability distribution is $P(x)\sim \exp(\alpha x)$. A
classical example of a problem of this type is sedimentation equilibrium, where
$\alpha$ is determined by temperature. In this work we do not introduce a
thermal reservoir and $\alpha$ is determined from the equation of motion. We
consider a general approach to determining $\alpha$ which is not always in
agreement with Einstein's relation between the mean velocity and the diffusion
coefficient. We illustrate our results with a model inspired by the Boltzmann
equation.
