Drift estimator
= Drift estimator
{title2=$\widehat b_T(x,h)$}
From a continuously observed <Itô diffusion>, a local drift estimator divides $\int_0^T\mathbf1_{[x-h,x+h]}(X_t)\,dX_t$ by the corresponding <diffusion occupation time>. Its error separates into a local <Hölder continuity> bias and an <Itô integral> divided by occupation time. The <Itô isometry> gives a pointwise noise scale $(Th)^{-1/2}$ when the invariant density is locally positive.