## Asymptotics in small time for the density of a stochastic differential equation driven by a stable Lévy process

Type:
Site:
Date:
26/04/2017 - 15:00 - 15:45
Salle:
P1 005
Directeur(s):
CLÉMENT Emmanuelle
Co-directeur(s):
Arnaud GLOTER
Localisation:
Université de Marne-la-vallée
Localisation:
France
Résumé:

This work focuses on the asymptotic behavior of the density in small time of a stochastic differential equation driven by an $\alpha$-stable process with index $\alpha \in (0,2)$. We assume that the process depends on a parameter $\beta=(\theta,\sigma)^T$ and we study the sensitivity of the density with respect to this parameter. This extends the results of Emmanuelle Clément and Arnaud Gloter which was restricted to the index $\alpha \in (1,2)$ and considered only the sensitivity with respect to the drift coefficient. By using Malliavin calculus, we obtain the representation of the density and its derivative as an expectation and a conditional expectation. This permits to analyze the asymptotic behavior in small time of the density, using the time rescaling property of the stable process.