Zhigailo O. Optimal estimation of the Markov systems under incomplete observations.

The dissertation is devoted to the development of a statistical analysis of hidden Markov models. The tasks of parametric and nonparametric estimation for the characteristics of partially observed Markov systems are solved. The recurrent algorithms of optimal estimation for the moments of hits of a Markov system and a number of such hits during the observations are constructed. The iterative procedure for finding maximum likelihood estimations in the case when the Markov process distribution depends on unknown parameters is obtained. The new task and methods of its solution in case when observations are incomplete and deformed are proposed. The obtained results are applied to the statistical analysis of the queuing systems under incomplete observations.