stochastic calculus - Units in Ornstein-Uhlenbeck(OU) process

Take an OU process characterized by

X(0) = x

dX(t) = - a X(t) dt + b dW(t)

where a,b >0. The parameter a is usually interpreted a dissipative term, and b is a volatility term.

My question is this: What are the units of a and b? Is it true that a is (time) ^-1 , and b is unitless? Then how can one make sense of the variance which approaches (b ² /(2 a)) as t goes to infinity?

Thanks for your help.