Before revision:  The formula is remarkably universal, as it holds for d-dimensional diffusion processes (i) with general space-dependent diffusivities and force fields, (ii) on any smooth Riemannian manifold , (iii) in the presence of reflecting obstacles, and (iv) with partially absorbing targets.
After revision:  The formula is remarkably universal, as it holds for d-dimensional diffusion processes (i) with general space-dependent diffusivities and force fields, (ii) on Riemannian manifolds , (iii) in the presence of reflecting obstacles, and (iv) with partially absorbing targets.