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Diffusions with measurement errors. II. Optimal estimators

Published online by Cambridge University Press:  15 August 2002

Arnaud Gloter
G.R.A.P.E., UMR 5113 du CNRS, Université Montesquieu (Bordeaux), Avenue Léon Duguit, 33608 Pessac, France;
Jean Jacod
Laboratoire de Probabilités et Modèles Aléatoires, UMR 7599 du CNRS, Université Paris 6, 4 place Jussieu, 75252 Paris, France;
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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.

Research Article
© EDP Sciences, SMAI, 2001

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