Pilipenko A. Evolutionary stochastic flows and measure-valued processes

The thesis is devoted to the construction and study of properties of stochastic flows generated by stochastic complex systems. Infinite-dimensional Liouville theorem is proved in different situations. It is considered not only deterministic case but stochastic flows also. We construct and study properties of flows that generated by stochastic flows with reflection on the boundary of a domain. The approximation theorem for flows with interaction is proved, the support of the distribution is characterized, properties of finite-dimensional distributions is studied. Conditions of existence for a stationary solutions are given and functional central limit theorem is proved.