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.