Efficient estimation for stochastic differential equations driven by a stable Lévy process

Orateur: Ngo Thi Bao Tram
Localisation: Université du Mans, France
Type: Groupe de travail probabilités
Site: UPEC
Salle: P2 131 (salle conseil)
Date de début: 06/02/2024 - 14:00
Date de fin: 06/02/2024 - 15:00

The joint parametric estimation of the drift coefficient, the scale coefficient and the jump activity in stochastic differential equations driven by a symmetric stable Lévy process is considered, based on high-frequency observations. Firstly, the LAMN property for the corresponding Euler type scheme is proved and lower bounds for the estimation risk in this setting is deduced. When the approximation scheme experiment is asymptotically equivalent to the original one, these bounds can be transferred. Secondly, a one-step procedure is proposed which is shown to be fast and asymptotically efficient. The performances in terms of asymptotical variance and computation time on samples of finite size are illustrated with simulations.