Optimal L2-approximation of occupation and local times for symmetric stable processes

Abstract

The $L^2$-approximation of occupation and local times of a symmetric α-stable Lévy process from high frequency discrete time observations is studied. The standard Riemann sum estimators are shown to be asymptotically efficient when $0<\mathit{\alpha }\le 1$, but only rate optimal for $1<\mathit{\alpha }\le 2$. For this, the exact convergence of the $L^2$-approximation error is proven with explicit constants.