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

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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https://hal.archives-ouvertes.fr/hal-03324325
Contributor : Ronan Le Guével Connect in order to contact the contributor
Submitted on : Wednesday, August 25, 2021 - 11:23:27 AM
Last modification on : Wednesday, June 1, 2022 - 3:13:04 AM
Long-term archiving on: : Friday, November 26, 2021 - 7:33:56 PM

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Randolf Altmeyer, Ronan Le Guével. Optimal L2 -approximation of occupation and local times for symmetric stable processes. Electronic Journal of Statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2022, 16, pp.2859 - 2883. ⟨10.1214/22-EJS2013⟩. ⟨hal-03324325⟩

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