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.