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Information × Registration Number 0224U031694, 0122U001730 , R & D reports Title Asymptotic properties of branching and evolutionary processes. popup.stage_title Head Iksanov Oleksandr М., Доктор фізико-математичних наук Registration Date 05-06-2024 Organization Taras Shevchenko National University of Kyiv popup.description2 We have proved a limit theorem for the derivative martingale associated with a branching random walk and derived theasymptoticof the distribution tail of a limiting random variable for the derivative martingale. The realization of this part of the research was made possible by finding a new representation of solutions to the Poisson equation on a half-line of at most linear growth. We have investigated dynamic models of the spread of epidemics with impulse impact, found the asymptotic of the corresponding evolutionary processes and analyzed the impact of rare epidemic outbreaks on the dynamics of infection spread. A new Kac-like modelon the complex plane has been considered and some moment characteristics of theprocess in focus have been obtained. Among other things, this enabled us to work out a new analytic approach to solving a Schrödinger-type equations. We have given a probabilistic representation of solutions to evolutionary kinetic-type equations with a nonhomogeneous smoothing transform on the right-hand side. Depending on the properties of the smoothing transform and the initial conditions two asymptotic regimes for solutions of the aforementioned evolutionary equations have been investigated. Our main technical tool has been the analysis of the underlying continuous-time branching random walks. Summarizing, we have obtained some new fundamental results in the theory of random processes, which are particularly used when constructing and analyzing models of evolutionary processes. It is expected that our methods will find applications in decision procedures related to the problems of countering information influences, in biomedical research, etc. Our results can be used to improve the efficiency of decision-making in modeling and analyzing evolutionary processes. Also, these can be used when preparing monographs and textbooks, lecture courses, etc., as well as in the framework of joint research projects with leading Ukrainian and foreign scientists. Product Description popup.authors Dovhyy Bohdan V. Marynych Oleksandr V. Samoilenko Ihor V. Samoilenko Oleksandra I. Usar Iryna Ya. popup.nrat_date 2024-06-05 Close