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Diffusions with measurement errors. II. Optimal estimators

Published online by Cambridge University Press:  15 August 2002

Arnaud Gloter  and
Jean Jacod
Arnaud Gloter
Affiliation:
G.R.A.P.E., UMR 5113 du CNRS, Université Montesquieu (Bordeaux), Avenue Léon Duguit, 33608 Pessac, France; gloter@montesquieu.u-bordeaux.fr.
Jean Jacod
Affiliation:
Laboratoire de Probabilités et Modèles Aléatoires, UMR 7599 du CNRS, Université Paris 6, 4 place Jussieu, 75252 Paris, France; jj@ccr.jussieu.fr.
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Abstract

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.

Keywords

Statistics of diffusionsmeasurement errorsLAN property.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 5 , 2001 , pp. 243 - 260
Copyright
© EDP Sciences, SMAI, 2001

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References

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