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 $