On drift parameter estimation for mean-reversion type stochastic differential equations with discrete observations

We study the parameter estimation for mean-reversion type stochastic differential equations driven by Brownian motion. The equations, involving a small dispersion parameter, are observed at discrete (regularly spaced) time instants. The least square method is utilized to derive an asymptotically consistent estimator. Discussions on the rate of convergence of the least square estimator are presented. The new feature of this study is that, due to the mean-reversion type drift coefficient in the stochastic differential equations, we have to use the Girsanov transformation to simplify the equations, which then gives rise to the corresponding convergence of the least square estimator being with respect to a family of probability measures indexed by the dispersion parameter, while in the literature the existing results have dealt with convergence with respect to a given probability measure