Samosonok O. Parameter estimation methods for Markov random processes with local interaction

This thesis is devoted to the investigation of network structures based on Markov random fields with local interaction between elements. Main attention is paid to the unknown parameter estimation methods, asymptotic properties of suggested estimates, practical and algorithmic problems of their calculation. Investigation results could be used either for theoretic interpretation of various phenomena in economics, biology, computer sciences or for solving applied tasks of stochastic processes simulation in logistical, transport and data transferring systems. During his research author has proven consistency of maximum likelihood estimator for unknown parameter of Gibbs distribution in case of independent observations and observations under strong mixing condition, found necessary conditions for asymptotic normality of such estimators, proved strong consistency and found asymptotic normality conditions of min square estimators. Based on stochastic quasi-gradient method iterative algorithm for maximum likelihood estimator of Gibbs distribution was suggested and original recurrent algorithm for root-cause analysis in communication network was applied. It is based on Markov process with local interaction theory.