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Information × Registration Number 0220U100681, 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 23-01-2020 Organization Taras Shevchenko National University of Kyiv popup.description2 The objects of study are multiple collision permutation coalescents, random trees, convex hulls of point random processes, evolutionary models in a random environment. The purpose 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 are modern methods of recovery theory, theory of correct change, stochastic and integral geometry, theory of random regenerative structures and random processes with immigration, etc. For coalescents with dust component and beta coalescents without dust component, a complete classification of the modes of weak convergence of the collision spectrum was obtained. Using the theory of multidimensional correct change, the theorem on continuous reflection, and the geometric properties of Poisson processes, a number of results on the asymptotics of spherical convex hulls and corresponding random cones were established. Studies related to recursive random trees have proved functional boundary theorems for their profiles by embedding special-type Cramp-Mod-Jaggers branching processes. Proof of weak convergence and dissipation problem for evolutionary models with stochastic applications is based on a new approach that requires asymptotic analysis of the respective operators.  Product Description popup.authors Iksanov Oleksandr М. Bogun Vladyslav A. Dovgay Bogdan V. Marynych Оleksandr V. Nikitin Anatolii V. Raschytov Bogdan S. Samoilenko Igor V. Trebina Nataliya M. Schestakov Sergiy S. popup.nrat_date 2020-04-02 Close