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2022 Optimal L2-approximation of occupation and local times for symmetric stable processes
Randolf Altmeyer, Ronan Le Guével
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Electron. J. Statist. 16(1): 2859-2883 (2022). DOI: 10.1214/22-EJS2013

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<α1, but only rate optimal for 1<α2. For this, the exact convergence of the L2-approximation error is proven with explicit constants.

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Randolf Altmeyer. Ronan Le Guével. "Optimal L2-approximation of occupation and local times for symmetric stable processes." Electron. J. Statist. 16 (1) 2859 - 2883, 2022. https://doi.org/10.1214/22-EJS2013

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Received: 1 August 2021; Published: 2022
First available in Project Euclid: 27 April 2022

Digital Object Identifier: 10.1214/22-EJS2013

Keywords: Lévy process , Local time , lower bound , occupation time , Stable process

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Vol.16 • No. 1 • 2022
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