LAMN PROPERTY FOR THE DRIFT AND VOLATILITY PARAMETERS OF A SDE DRIVEN BY A STABLE LEVY PROCESS

Abstract : This work focuses on the Local Asymptotic Mixed Normality (LAMN) property from high frequency observations, of a continuous time process solution of a stochastic differential equation driven by a pure jump Lévy process with index α ∈ (0, 2). The process is observed on the fixed time interval [0,1] and the parameters appear in both the drift coefficient and scale coefficient. This extends the results of [5] where the index α ∈ (1, 2) and the parameter appears only in the drift coefficient. We compute the asymptotic Fisher information and find that the rate in the LAMN property depends on the behavior of the Lévy measure near zero. The proof relies on the small time asymptotic behavior of the transition density of the process obtained in [6].
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https://hal.archives-ouvertes.fr/hal-01472749
Contributor : Emmanuelle Clément <>
Submitted on : Tuesday, February 21, 2017 - 11:39:45 AM
Last modification on : Thursday, July 18, 2019 - 3:00:05 PM
Long-term archiving on : Monday, May 22, 2017 - 2:34:58 PM

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Emmanuelle Clément, Arnaud Gloter, Huong Nguyen. LAMN PROPERTY FOR THE DRIFT AND VOLATILITY PARAMETERS OF A SDE DRIVEN BY A STABLE LEVY PROCESS. 2017. ⟨hal-01472749v1⟩

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