Diffusion occupation time
= Diffusion occupation time
{title2=$A_T(I)$}
The time spent by a <Itô diffusion> in a measurable set $I$ up to time $T$ is $A_T(I)=\int_0^T\mathbf1_I(X_t)\,dt$. 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>.