Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Diffusions with measurement errors. II - Optimal estimators


Code(s) de Classification MSC:

Résumé: We consider a diffusion process $X$ which is observed at times $i/n$ for $i=0,1,\ldots,n$, each observation being subject to a measurement error. All errors are independent and centered Gaussian with known variance $\r_n$. There is an unknown parameter to estimate within the diffusion coefficient. In this second paper we construct estimators which are asymptotically optimal when the process $X$ is a Gaussian martingale, and we conjecture that they are also optimal in the general case.

Mots Clés: Statistics of diffusions ; measurement errors ; LAN property

Date: 2000-11-21

Prépublication numéro: PMA-624