Consistency and asymptotic normality of maximum likelihood estimation for Gaussian Markov processes from discrete observations

In this paper we prove the weak consistency and the asymptotic normality of the maximum likelihood estimation based on discrete observations ofn independent Gaussian Markov processes. The Ornstein Uhlenbeck process is a special Gaussian Markov process. We derive asymptotic simultaneous confidence regions for the parameters of the Ornstein Uhlenbeck process as an application.