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Information × Registration Number 0226U002569, (0123U101997) , R & D reports Title Development of stochastic models, statistical methods for analysis and optimization of systems in the medical and socio-economic spheres popup.stage_title Аналіз властивостей побудованих моделей та алгоритмів. Head Iryna V. Rozora, Доктор фізико-математичних наук Registration Date 27-02-2026 Organization Taras Shevchenko National University of Kyiv popup.description1 Construction and research of stochastic models of processes that describe the functioning of systems in the medical sphere, solving the optimal control problems for the corresponding service processes in a dynamic mode. Research of the stationary regime existence conditions and calculation of the main efficiency characteristics for multidimensional Markov chains with continuous time as models of medical institutions, support systems, etc. These results will allow solving the problem of choosing the optimal structure of equipment and personnel, synthesizing optimal strategies for managing service processes, and developing software for optimal management of real systems. popup.description2 The study presents comprehensive results in the modeling, analysis, and optimization of stochastic systems of various natures. Systems with retrial calls and hysteresis-based policies are investigated; conditions for the existence of a stationary regime are established, and explicit formulas for stationary probabilities are derived. This enables more accurate assessment of convergence and the solution of optimal control problems. A comprehensive method for the statistical analysis of the impulse response function of linear systems is developed. The method is based on the integral cross-correlogram and makes it possible to evaluate the function’s properties, asymptotic behavior, and convergence, as well as to test statistical hypotheses using a nonparametric goodness-of-fit criterion. An adaptive algorithm for sequential resource allocation, DTS-OC, is proposed. It ensures robustness to data drift in nonstationary environments through discounting and a mechanism that reduces the impact of erroneous clustering. Multichannel stochastic networks with periodically varying input flow rate are studied, and models of the stationary regime are obtained, along with analytical formulas for the mean profit and risk. An analysis of machine learning models for predicting echocardiographic parameters from ECG data is conducted, demonstrating the promise of ensemble methods. A Markov model of the HIV/AIDS diagnostic process is developed; transition matrices in discrete and continuous time are estimated, censored distributions are reconstructed, and confidence intervals for the number of people living with HIV/AIDS are constructed. A cluster analysis of economic characteristics of 54 world cities is performed, demonstrating the effectiveness of combining agglomerative and spectral clustering to reveal complex data structures. In addition, new results are obtained on stability and regularization in vector optimization problems with quadratic criteria. Product Description popup.authors Dmytro V. Zatula Pavlo S. Knopov Iryna Y. Usar Hanna V. Livinska Mykhailo M. Sharapov Mariia V. Losieva Olha V. Lukovych Olha I. Vasylyk Vadym D. Ponomarov Illia A. Chaikovskyi Nataliia V. Semenova Nataliia M. Hryhorieva Antonina H. Pererva Oleksii O. Frankov Anastasiia O. Melnyk popup.nrat_date 2026-02-27 Close