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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/nfor i = 0,1,...,n, each observation being subject to a measurementerror. All errors are independent and centered Gaussian with knownvariance pn . There is an unknown parameter to estimate within thediffusion coefficient. In this second paper weconstruct estimators which are asymptotically optimal when theprocess X is a Gaussian martingale, and we conjecture that they arealso optimal in the general case.

Keywords

Statistics of diffusionsmeasurementerrorsLAN property.

Information

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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