Asymptotic properties of Maximum likelihood Estimators (MLEs) for the non-parametric and parametric Markov chains have been studied by Basawa and Rao (1980), AI-Eideh et. at (1988) and others. In this paper we present a complete proof of the property of asymptotic normality of MLE's for the non-parametric Markov chains. Some gaps and details must be filled out.
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