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Information × Registration Number 0221U102334, 0119U100338 , R & D reports Title Development of new mathematical methods for analysis and optimization of systems under uncertainty. popup.stage_title Head Nakonechnyi Oleksandr G., Доктор фізико-математичних наук Registration Date 01-02-2021 Organization Taras Shevchenko National University of Kyiv popup.description2 Object of research: systems of equations of different types, stochastic equations, uncertainty, stochastic service networks, random processes, diseases. Purpose: development of new asymptotic methods of analysis and optimization of systems in conditions of uncertainty. Research methods: modern methods of decision theory in conditions of uncertainty, asymptotic methods, new methods of system analysis and optimization of stochastic and deterministic systems, modern methods of group theory. Representations are obtained for guaranteed a posteriori and a priori estimates and errors of estimation of unknown solutions and data due to solutions of some ordinary differential equations of special form. Representations of minimax estimates for hyperbolic equations with rapidly oscillating coefficients are obtained and their closeness to the estimates of the corresponding equations with averaged parameters is investigated. The conditions for the weak convergence of the evolution equation with the momentum perturbation in the Levy approximation scheme and the control with the equilibrium point of the function of the quality criterion for which the stochastic approximation procedure is constructed are obtained. Stochastic networks, which receive input flows of requirements with time-dependent intensity, are studied, and the quasi-stationary mode of operation is analyzed. Under critical load conditions, the convergence of the service process to the Gaussian process in a uniform topology is proved. Correlation characteristics of the boundary process are written through the network parameters. Hyperboleans have been studied and the problem of rigidity has been solved. Numerical methods for solving boundary value problems with random initial and boundary conditions using methods of statistical modeling of Gaussian random processes and fields are developed, the conditions of convergence of the developed algorithms are investigated. Product Description popup.authors Zinko Taras P. Kapustyan Olena A. Korobko Tetyana V. Kudin Hryhoriy І. Livinska Hanna V. Losyeva Mariya V. Nikitin Anatoliy V. Naumenko Yurii O. Podlipenko Yury K. Protasov Igor V. Protasova Kseniia D. Chikrii Arkadii О. Shevchuk Yuliia M. popup.nrat_date 2021-02-01 Close