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

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 60J60 Diffusion processes, See also {58G32}
- 62F12 Asymptotic properties of estimators
- 62M05 Markov processes: estimation

**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*