Diffusion occupation time ($A_T(I)$)

The time spent by a Itô diffusion in a measurable set $I$ up to time $T$ is $A_T(I)={\int }_0^T{1}_I(X_t)dt$. Under stationarity its expected value is $T\mu (I)$, where $\mu$ is the Invariant distribution of an Itô diffusion. Occupation times form the denominator of a local drift estimator.