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Information × Registration Number 0225U003125, (0122U001843) , R & D reports Title Stochastic dynamical systems, inhomogeneous in time or random time: asymptotics and statistical analysis popup.stage_title Аналіз властивостей побудованих моделей та алгоритмів. Head Mishura Yuliia S., Доктор фізико-математичних наук Registration Date 21-05-2025 Organization Taras Shevchenko National University of Kyiv popup.description1 Investigation of general dynamical systems modeled by random processes, in particular, Levy processes, inhomogeneous Markov processes, random time processes, processes arising as solutions of partial differential derivatives and random initial conditions, and equations with generalized fractional operators. popup.description2 The relevance lies in the fact that the results for fractional processes and their entropic properties will allow us to more accurately describe and model financial, physical, and technical systems with long-term dependence; the application of the results for heterogeneous Markov processes will improve the quality of models in problems of actuarial mathematics, the theory of mass service, and the theory of risk; processes with random time replacement are needed for the analysis of biological, medical, environmental, and financial data, and in the theory of reliability. Purpose of the work: study of general dynamical systems modeled by random processes, in particular, Lévy processes, heterogeneous Markov processes, processes with random time, processes that arise as solutions of partial differential equations with random initial conditions, and equations with generalized fractional operators. The main objectives of the project: To build new methods of statistical estimation in models with errors and functional nonlinear models, to establish asymptotic properties of estimates. To establish the properties of Gaussian Volterra processes, entropy characteristics of fractional processes. To construct an algorithm for modeling the moment of exit of the Lévy process from the domain, to apply an algorithm for estimating functionals from processes. To construct stability estimates, recovery time estimates, which can be used in specific models for solving applied problems. To derive statistical estimates of functionals from solutions of differential equations with random initial conditions, convenient for practical use. To investigate new classes of processes with random time change, to establish equations for their one-dimensional distributions and other characteristics of their distributions. Product Description popup.authors Bodnarchuk Iryna M. Borysenko Oleksandr D. Holomozyi Vitalii V. Knopova Viktoriia P. Svitlana V. Kushnirenko Lukovych Olha V. Maiboroda Rostyslav Ye. Mokliachuk Tetiana O. Sakhno Liudmyla M. Tymoshek Tetiana R. Shkliar Serhii V. popup.nrat_date 2025-05-21 Close