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

Thị Bảo Trâm NGÔ
Université d'Évry

Date(s) : 07/10/2025 iCal
14h30 - 15h30

The joint parametric estimation of the drift coefficient,
the scale coefficient, and the jump activity index
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 proven,
and lower bounds for the estimation risk in this setting are deduced.
Therefore, when the approximation scheme experiment is asymptotically equivalent
to the high-frequency observation of the solution
of the considered stochastic differential equation,
these bounds can be transferred.
Secondly, since the maximum likelihood estimator can be time-consuming
for large samples, an alternative Le Cam’s one-step procedure is proposed
in the general setting.
It is based on an initial guess estimator,
which is a combination of generalized variations
of the trajectory for the scale and the jump activity index parameters,
and a maximum likelihood-type estimator
for the drift parameter.
This proposed one-step procedure is shown to be fast,
asymptotically normal, and even asymptotically efficient
when the scale coefficient is constant.
In addition, the performances
in terms of asymptotic variance and computation time
on samples of finite-size are illustrated with simulations.
This talk is based on joint work
with Alexandre Brouste and Laurent Denis.