The Ornstein-Uhlenbeck process is defined as
$$ \frac{d}{dt}x(t) = -\frac{1}{\mu}x + \sqrt{\frac{2\sigma^2}{\mu}}\xi(t) $$
where $\xi(t)$ is a unit white noise.
What are the units the parameters? Lets say $x$ is dimensionless. Then the left-hand side must have dimensions 1/time, which means $\mu$ must have units of time.
Now if $\xi$ is also dimensionless, then $\sigma^2$ must have units 1\time. Is this correct?