FIRST HITTING TIMES AND POSITIONS OF CONCENTRIC SPHERESFOR TESTING THE DRIFT OF A DIFFUSION PROCESS
V. Genon-Catalot
Abstract: Consider a diffusion process on with drift vector
depending of an unknown real parameter with small known variance matrix The
aim of this paper is testing vs with from the observation of the first
hitting times and positions of concentric spheres centered at with radii for
given We obtain the asymptotic behaviour of this process as when the trajectory
of the corresponding dynamical system leaves any sphere centered at within
finite time. We then construct a test on and study its asymptotic properties by
means of contiguity. When the test is locally asymptotically most powerful
(LAMP). We also consider a test based on the first hitting times of spheres only.
a diffusion process on 
with drift vector 
depending of an unknown real parameter 
with small known variance matrix 
The
aim of this paper is testing 
vs 
with 
from the observation of the first
hitting times and positions of concentric spheres centered at 
with radii 
for
given 
We obtain the asymptotic behaviour of this process as 
when the trajectory
of the corresponding dynamical system leaves any sphere centered at 
within
finite time. We then construct a test on 
and study its asymptotic properties by
means of contiguity. When 
the test is locally asymptotically most powerful
(LAMP). We also consider a test based on the first hitting times of spheres only.