Diffusions with measurement errors. I. Local Asymptotic Normality
Arnaud Gloter, Jean Jacod (2010)
ESAIM: Probability and Statistics
Similarity:
We consider a diffusion process which is observed at times for = 0,1,...,, each observation being subject to a measurement error. All errors are independent and centered Gaussian with known variance . There is an unknown parameter within the diffusion coefficient, to be estimated. In this first paper the case when is indeed a Gaussian martingale is examined: we can prove that the LAN property holds under quite weak smoothness assumptions, with an explicit limiting Fisher information....