Discretely observed diffusions: Classes of estimating functions and small Delta-optimality

Ergodic diffusions in several dimensions, depending on an unknown multivari ate parameter are considered. For estimation, when the diffusion is observe d only at finitely many equidistant time points, unbiased estimating functi ons leading to consistent and asymptotically Gaussian estimators are used. Different types of estimating functions are discussed and the concept of sm all Delta -optimality is introduced to help select good estimating function s. Explicit criteria for small Delta -optimality are given. Also some exact optimality conditions are presented as well as, for one-dimensional diffus ions, methods for improving estimators using time reversibility.