We consider a one-dimensional ergodic diffusion process, whose drift depends on an unknown parameter. A way to estime θ from the observation of the process at n equidistant times kδ, as δ is near 0 but fixed and n goes to infinity, is to construct an approximation to the likelihood function. Each transition density can be replaced by a Gaussian density, whose mean is an approximation in o(δ**p) to the conditional expectation. For that purpose, we propose a p-order adapted and approximative discrete-time scheme of diffusion process. Under some general assumptions, we obtain an asymptotically normal estimator for an approximation of order δ**p to θ .
Publié le : 1997-07-05
Classification:
schéma d'approximation adapté à l'ordre p,
Processus de diffusion,
estimation par minimum de contraste,
espérance conditionnelle,
schéma d'approximation adapté à l'ordre p.,
62 M 05 - 62 F 12,
[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST],
[STAT.TH]Statistics [stat]/Statistics Theory [stat.TH]
@article{hal-00276877,
author = {Souchet, Sandie},
title = {Sch\'ema d'approximation adapt\'e \`a l'ordre p et Estimation du param\`etre de d\'erive d'une diffusion.},
journal = {HAL},
volume = {1997},
number = {0},
year = {1997},
language = {fr},
url = {http://dml.mathdoc.fr/item/hal-00276877}
}
Souchet, Sandie. Schéma d'approximation adapté à l'ordre p et Estimation du paramètre de dérive d'une diffusion.. HAL, Tome 1997 (1997) no. 0, . http://gdmltest.u-ga.fr/item/hal-00276877/