Estimating functions for SDE driven by stable Lévy processes

Abstract : This paper is concerned with parametric inference for a stochastic differential equation driven by a pure-jump Lévy process, based on high frequency observations on a fixed time period. Assuming that the Lévy measure of the driving process behaves like that of an α-stable process around zero, we propose an estimating functions based method which leads to asymptotically efficient estimators for any value of α ∈ (0, 2) and does not require any integrability assumptions on the process. The main limit theorems are derived thanks to a control in total variation distance between the law of the normalized process, in small time, and the α-stable distribution. This method is an alternative to the non Gaussian quasi-likelihood estimation method proposed by Masuda [20] where the Blumenthal-Getoor index α is restricted to belong to the interval [1, 2).
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Contributor : Emmanuelle Clément <>
Submitted on : Thursday, June 14, 2018 - 9:57:21 AM
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Emmanuelle Clément, Arnaud Gloter. Estimating functions for SDE driven by stable Lévy processes. 2018. ⟨hal-01570175v2⟩

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