Diffusions with measurement errors. II. Optimal estimators
ESAIM: Probability and Statistics, Tome 5 (2001), pp. 243-260.

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 ${\rho }_{n}$. 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.

Classification : 60J60,  62F12,  62M05
Mots clés : statistics of diffusions, measurement errors, LAN property
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Gloter, Arnaud; Jacod, Jean. Diffusions with measurement errors. II. Optimal estimators. ESAIM: Probability and Statistics, Tome 5 (2001), pp. 243-260. http://www.numdam.org/item/PS_2001__5__243_0/

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