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 truncated α -stable 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 L ́evy 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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Article dans une revue
ESAIM: Probability and Statistics, EDP Sciences, 2018, 〈10.1051/ps/2018007 〉
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https://hal.archives-ouvertes.fr/hal-01703970
Contributeur : Emmanuelle Clément <>
Soumis le : jeudi 8 février 2018 - 10:39:17
Dernière modification le : vendredi 23 novembre 2018 - 12:17:06

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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. ESAIM: Probability and Statistics, EDP Sciences, 2018, 〈10.1051/ps/2018007 〉. 〈hal-01703970〉

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