Maximnm contrast estimation for diffusion processes from discrete observations

We consider a one-dimensional diffusion process (Xt) with drift b{θ&, u) depending on an unknown parameter # and small known diffusion coefficient, s. The sample path is observed at times k△A, =0, 1, …,. N up to T=NA, for fixed T. We study maximum contrast estimators (m. c. e. ) of θ based on this observation with asymptotic results as e and ^ go to 0 simultaneously. We specify conditions on △A under which the ni. e. e. are asymptotically normal and asymptotically equivalent to the maximum Hkelihood estimator of