We consider a diffusion model for which the drift b is Lipschitz continuous on R but its derivative is not continuous in ro. Our aim is to estimate this threshold parameter from discrete observations at step h_n of the stationary and ergodic process. The least squares method based on the approximate discrete-time Euler's scheme provides a consistent estimator when n*h_n goes to infinity and h_n to 0 . Moreover if n*(h_n)**3 goes to 0, this estimator is asymptotically normal with a standard rate.
Publié le : 1999-07-05
Classification:
temps local,
Schéma d'approximation d'Euler,
estimateur des moindres carrés,
modèle à seuil,
diffusion stationnaire et ergodique,
temps local.,
62 M 05 - 62 F 12,
[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST],
[STAT.TH]Statistics [stat]/Statistics Theory [stat.TH]
@article{hal-00276902,
author = {Souchet, Sandie},
title = {Estimation du param\`etre de d\'erive d'une diffusion sous des conditions d'irr\'egularit\'e de la d\'erive.},
journal = {HAL},
volume = {1999},
number = {0},
year = {1999},
language = {fr},
url = {http://dml.mathdoc.fr/item/hal-00276902}
}
Souchet, Sandie. Estimation du paramètre de dérive d'une diffusion sous des conditions d'irrégularité de la dérive.. HAL, Tome 1999 (1999) no. 0, . http://gdmltest.u-ga.fr/item/hal-00276902/