Local Asymptotic Mixed Normality property for discretely observed stochastic differential equations driven by stable Levy processes

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:125

Article

Clement, Emmanuelle¹  Gloter, Arnaud² 

[1] Univ Paris Est, Lab Anal & Math Appl, F-77454 Marne La Vallee 2, France

[2] Univ Evry Val dEssonne, Lab Math & Modelisat Evry, UMR 8071, F-91037 Evry, France

关键词: Local Asymptotic Mixed Normality Property;    Levy process;    Stable process;    Malliavin calculus for jump processes;   

DOI  :  10.1016/j.spa.2015.01.002

来源: Elsevier

【 摘 要 】

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 Levy 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. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

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