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Information × Registration Number 0220U101165, 0119U100317 , R & D reports Title Exact formulas, estimates, asymptotic properties, and statistical analysis of complex evolutionary systems with many degrees of freedom. popup.stage_title Head Mishura Yulija Stepanivna, Доктор фізико-математичних наук Registration Date 04-01-2020 Organization Taras Shevchenko National University of Kyiv popup.description2 Object of study - random processes and fields, stochastic differential equations, diffusion models with stochastic volatility, financial markets, regression models. Aim of work - development of theory of fractional processes, construction of stochastic analysis for non-Gaussian random noise, investigation of properties of solutions of wave equations with general stochastic measures and equations of thermal conductivity with random factors, study of spatiotemporal fields in the sphere, improvement of methods of estimation of parameters conditions of consistency of estimates of parameters of homoscedastic linear models, study of actuarial and financial measures of risk. Research methods - analytical methods of probability theory and mathematical statistics, stochastic analysis methods, statistical modeling of random processes and fields, optimization theories and numerical methods. Main results of the research obtained in the work: It is proved that fractional processes of Cox-Ingersoll-Ross type with small Hurst indices are inalienable and have a positive probability of zero. A model of a financial market with fast-moving stochastic volatility is constructed, its arbitrage is proved with certain coefficients constraints, and the price of simple and exotic options is found in such a financial market. It is color-coded in time and white in space random noise with heavy distribution tails, integration with such random noise. New estimates have been established for the distribution of sub-sums of random fields, which are defined as the solutions of differential equations of the type of thermal conductivity with random initial conditions represented by the ph-sub-Gaussian harmonized processes. We construct a soft solution of a three-dimensional wave equation with a stochastic general measure and set its properties. The principle of averaging for the equation of oscillation of the strings with fixed ends, controlled by a stochastic measure, is investigated.  Product Description popup.authors Bondarchuk Iryna M. Zubchenko Volodymyr P. Kozachenko Yurii V. Kukush Оleksandr G. Mishura Yuliya S. Moklyachuk Мyhaylo P. Ragulina Elena Yu. Ralchenko Kostiantyn V. Sakhno Liudmyla M. Shevchenko Georgiy M. Shkliar Seriy V. popup.nrat_date 2020-04-02 Close