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Local Asymptotic Mixed Normality property for discretely observed stochastic differential equations driven by stable L\'evy processes

Abstract : We prove the Local Asymptotic Mixed Normality property from high frequency observations, of a continuous time process solution of a stochastic differential equation driven by a pure jump L´evy process. The process is observed on the fixed time interval [0, 1] and the parameter appears in the drift coefficient only. We compute the asymptotic Fisher information and find that the rate in the LAMN property depends on the behavior of the Levy measure near zero. The proof of this result contains a sharp study of the asymptotic behavior, in small time, of the transition probability density of the process and of its logarithm derivative.
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https://hal-upec-upem.archives-ouvertes.fr/hal-01141511
Contributor : Emmanuelle Clément <>
Submitted on : Monday, April 13, 2015 - 10:50:30 AM
Last modification on : Thursday, May 28, 2020 - 2:04:38 PM

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Emmanuelle Clément, Arnaud Gloter. Local Asymptotic Mixed Normality property for discretely observed stochastic differential equations driven by stable L\'evy processes. Stochastic Processes and their Applications, Elsevier, 2015, 123 (6), pp.2316-2352. ⟨10.1016/j.spa.2015.01.002⟩. ⟨hal-01141511⟩

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