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

2021/08/26 by Randolf Altmeyer, Altmeyer, Randolf, Ronan Le Guével +1
Economics, Econometrics and Finance · #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications

paper · doi:10.48550/arxiv.2108.11632

openalex publication_date 2021/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The L2-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 L2-approximation error is proven with explicit constants.

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