Diffusions with measurement errors. II. Optimal estimators

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 rho_n. There is an unknown parameter to estimate within the di usion 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.