New statistical investigations of the ornstein-uhlenbeck process

An asymptotic analysis is presented for estimation in the three-parameter Ornstein-Uhlenbeck process, where the parameters are the local mean, the drift, and the variance. We are interested in the case when the damping parameter (λ, or λT = κ) is nearly zero. The asymptotic sufficient statistics can be related to noncentral χ12 distribution. The maximum likelihood estimate of the parameter vector is a solution of a rather complicated system of equations. We describe the methods for solving maximum-likelihood equations. Classical and robust estimators are determined for parameters. It is shown that the lower confidence limit of the drift (or damping) parameter is equal to zero with positive probability when it is near to zero.