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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

G. Dohnal, On estimating the diffusion coefficient. J. Appl. Probab. 24 (1987) 105-114.
V. Genon-Catalot and J. Jacod, On the estimation of the diffusion coefficient for multidimensional diffusion processes. Ann. Inst. H. Poincaré Probab. Statist. 29 (1993) 119-153.
A. Gloter and J. Jacod, Diffusion with measurement error. I. Local Asymptotic Normality (2000).
J. Jacod and A. Shiryaev, Limit Theorems for Stochastic Processes. Springer-Verlag, Berlin (1987).
J. Jacod, On continuous conditional Gaussian martingales and stable convergence in law, Séminaire Proba. XXXI. Springer-Verlag, Berlin, Lecture Notes in Math. 1655 (1997) 232-246. CrossRef
M.B. Malyutov and O. Bayborodin, Fitting diffusion and trend in noise via Mercer expansion, in Proc. 7th Int. Conf. on Analytical and Stochastic Modeling Techniques. Hamburg (2000).
Renyi, A., On stable sequences of events. Sankya Ser. A 25 (1963) 293-302.