Samoilenko I. Analysis of asymptotic properties of complex evolutionary systems in a scheme of Poisson approximation

The thesis is devoted to the system analysis of some classes of processes, that model complex stochastic systems in a random medium, and to the investigation of their asymptotic properties. The system analysis is conducted from the point of view of their weak convergence, solution of large deviations problem, obtaining of asymptotic expansions. The methods of structuring, modelling and analysis of complex systems are developed, that means construction of mathematical algorithms for simplification of a complex system under preservation of its properties. The algorithm that allows to obtain explicitly the operators for description of the limit process in the scheme of Poisson approximation is constructed. The new methods and explicit algorithms, that use optimal control theory and convex analysis methods, are developed for the analysis of large deviations problem for the processes in the scheme of Poisson approximation and phase merging scheme. Asymptotical methods developed are applied to asymptotic analysis of some practical models. Analysis of limit behaviour of some conflict systems is conducted.