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 < α ≤ 1, but only rate optimal for 1 < α ≤ 2. For this, the exact convergence of the L 2 -approximation error is proven with explicit constants.