Diffusions with measurement errors. I. Local asymptotic normality
Arnaud Gloter, Jean Jacod (2001)
ESAIM: Probability and Statistics
Similarity:
We consider a diffusion process which is observed at times for , 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. What...