Volume 5, 2001
|Page(s)||243 - 260|
|Published online||15 August 2002|
Diffusions with measurement errors. II. Optimal estimators
G.R.A.P.E., UMR 5113 du CNRS, Université Montesquieu (Bordeaux), Avenue Léon Duguit, 33608 Pessac,
2 Laboratoire de Probabilités et Modèles Aléatoires, UMR 7599 du CNRS, Université Paris 6, 4 place Jussieu, 75252 Paris, France; email@example.com.
Revised: 24 October 2001
We consider a diffusion process X which is observed at times i/n for i = 0,1,...,n, each observation being subject to a measurement error. All errors are independent and centered Gaussian with known variance pn. 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.
Mathematics Subject Classification: 60J60 / 62F12 / 62M05
Key words: Statistics of diffusions / measurement errors / LAN property.
© EDP Sciences, SMAI, 2001
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