Parameter Estimation with Exact Distribution for Multidimensional Ornstein–Uhlenbeck Processes

It is shown that the suitably normalized maximum likelihood estimators of some parameters of multidimensional Ornstein–Uhlenbeck processes with coefficient matrix of a special structure have exactly a normal distribution. This result provides a generalization to an arbitrary dimension of the well-known behavior of the estimator of the period of a complex AR(1) process.