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Information × Registration Number 0221U102337, 0119U100321 , R & D reports Title Asymptotic and structural analysis of stochastic models of population dynamics. popup.stage_title Head Iksanov Oleksandr М., Доктор фізико-математичних наук Registration Date 01-02-2021 Organization Taras Shevchenko National University of Kyiv popup.description2 Objects of research - branched random walks, random walks in sparse random media, Markov chains associated with random series generated by linear recursion, models of information struggle. The aim of the work is to solve a number of open problems for classes of stochastic processes that characterize the dynamics of evolutionary mechanisms in populations, as well as to study their qualitative properties. Research methods - modern methods of recovery theory, the theory of correct change, the theory of branching processes in random environments, the theory of martingales. The criterion of zero-recurrence / transient Markov chains associated with random series generated by linear recursion is proved in the critical mode, when the random series are divergent. A new construction of solutions of kinetic equations by means of branched random walks in continuous time is proposed. Using this construction, the stationary solutions of the kinetic equations in the critical case are investigated. The criteria of convergence in Lp, p> 1, Biggins martingales with a complex parameter in the supercritical case are obtained. A number of boundary theorems for random walks in moderately and strongly sparse random media are proved. Based on the results of asymptotic analysis of evolution equations with random effects, the classical model of information struggle is generalized in order to study the impact of migration processes and rare information "explosions".  Product Description popup.authors Bohun Vladyslav A. Dovgay Bogdan V. Marynych Oleksandr V. Nikitin Anatolii V. Raschytov Bogdan S. Samoylenko Ihor V. Trebina Nataliya M. Shestakov Sergiy S. Yurachkivsʹkyy Andriy Р. popup.nrat_date 2021-02-01 Close