B2043
Title: Efficient estimation of stochastic differential equations driven by a stable Levy process
Authors: Alexandre Brouste - Le Mans University (France)
Emmanuelle Clement - Universite Gustave Eiffel (France)
Laurent Denis - Le Mans University (France)
Thi Bao Tram Ngo - University of Evry Val d Essonne (France) [presenting]
Abstract: We study the Local Asymptotic Mixing Normality (LAMN) property for stochastic differential equations driven by a stable Levy process, in which the joint parametric estimation of the drift coefficient, the scale coefficient and the jump activity of the process based on high frequency observations of the process on a fixed time interval is considered. We get this property by proving LAMN property for the corresponding Euler scheme with the ordinary differential equation. With the LAMN property obtained, we show that the one-step estimator is efficient and can exhibit quite similar finite-sample performance as the maximum likelihood estimator. We illustrate our results by numerical simulations.
