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 Clément and Gloter [Stoch. Process. Appl. 125 (2015) 2316–2352] 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 Clément et al. [Preprint HAL-01410989v2 (2017)].
Accepté le :
DOI : 10.1051/ps/2018007
Mots-clés : Lévy process, stable process, Malliavin calculus for jump processes, LAMN property, parametric estimation
@article{PS_2019__23__136_0,
author = {Cl\'ement, Emmanuelle and Gloter, Arnaud and Nguyen, Huong},
title = {LAMN property for the drift and volatility parameters of a sde driven by a stable {L\'evy} process},
journal = {ESAIM: Probability and Statistics},
pages = {136--175},
publisher = {EDP-Sciences},
volume = {23},
year = {2019},
doi = {10.1051/ps/2018007},
mrnumber = {3945580},
zbl = {1416.60052},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ps/2018007/}
}
TY - JOUR AU - Clément, Emmanuelle AU - Gloter, Arnaud AU - Nguyen, Huong TI - LAMN property for the drift and volatility parameters of a sde driven by a stable Lévy process JO - ESAIM: Probability and Statistics PY - 2019 SP - 136 EP - 175 VL - 23 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2018007/ DO - 10.1051/ps/2018007 LA - en ID - PS_2019__23__136_0 ER -
%0 Journal Article %A Clément, Emmanuelle %A Gloter, Arnaud %A Nguyen, Huong %T LAMN property for the drift and volatility parameters of a sde driven by a stable Lévy process %J ESAIM: Probability and Statistics %D 2019 %P 136-175 %V 23 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps/2018007/ %R 10.1051/ps/2018007 %G en %F PS_2019__23__136_0
Clément, Emmanuelle; Gloter, Arnaud; Nguyen, Huong. LAMN property for the drift and volatility parameters of a sde driven by a stable Lévy process. ESAIM: Probability and Statistics, Tome 23 (2019), pp. 136-175. doi : 10.1051/ps/2018007. http://archive.numdam.org/articles/10.1051/ps/2018007/
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