Schéma d'approximation adapté à l'ordre p et Estimation du paramètre de dérive d'une diffusion.

Overview & Synopsis

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 .