On Maximum Likelihood Estimation of the Markov Process

The maximum likelihood estimators of the unknown parameters of the stationary Gaussian Markov process are obtained. The likelihood function of the observations is derived. It conta-ins the unknown parameters, the mean (m), the parameter (0) and the vamiance (02) of the white noise process. It is found that the likelihood equations can obtained but the solutions of them are not easily. Instead of it we drive the conditional like-: tihood function. The conditional maicimum likelihood estimators are obtained. The limits of these es)imators when the mean equal to zero is equal to that obtained by the author (see (1]).
When the mean equal to zero the exact likelihood function, the likelihood equations and the maximum likelihood estimators are obtained, The Mout-Carlo method is used to investigate and to compare the estimators obtained here with that obtained before. The results indicate that the estimators obtained in this paper is better than Walker's estimators in most cases and are the same in other cases.