ON THE ESTIMATION OF THE DIFFUSION-COEFFICIENT FOR MULTIDIMENSIONAL DIFFUSION-PROCESSES

If a diffusion process has a diffusion coefficient which depends on a parameter theta, one can construct consistent sequences of estimators of theta based on the observation of the process at only n times, as n goes to infinity. Here we construct such estimators, and study their asymptotic efficiency. Of special interest to us are the multi-dimensional case (for the process) and the consideration of rather general sampling schemes.