Abstract. A mathematical model of some stochastic hierarchical structure is presented and several problems of the statistical estimations in the case of incomplete observations are considered. A method to construct consistent estimators of parameters for hidden Markov model using the structure of correlation dependence of Markov chains is explained. Such models often occur in applied fields of stochastic processes theory such as queuing theory, inventory control theory, risk theory, etc. The paper contains specific examples of parametric estimation for models in the above-mentioned scientific domains.

Keywords: Markov chain, hidden Markov model, queuing system, statistical estimation, consistent estimators.