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Information × Registration Number 0214U006979, 0111U006561 , R & D reports Title Evolutionary systems: analytical study of transformations by the random fluctuation and statistical regularities popup.stage_title Head Mishura Yuliya Stepanivna, Registration Date 23-04-2014 Organization Taras Shevchenko Kiev university popup.description2 Object of study - random processes and fields , stochastic differential equations , financial markets, risk processes . Purpose - to study the properties of fractional Brownian motion and related processes and stochastic differential equations ; research tasks filtering , restoration and expansion in different vayvlet -basis for fractional Brownian motion; construction potrayektornyh integrals for stable processes; creating effective modifications developed algorithms evolutionary statistics systems; development of stochastic models in problems of actuarial and financial mathematics. Research methods - analytical methods of probability theory and mathematical statistics, stochastic simulation. The main research results obtained in the paper : We prove the theorem for extreme functional multiplicative scheme of financial markets, showing the conditions of existence and appearance of the diffusion approximation. Found parameter estimation bias in the mixed Brownian - fractional Brownian model. Conditions for uniform convergence of wavelet expansions Gaussian random processes. The results of the rate of convergence of wavelet expansions in the space C ([0 , T]). Investigated the asymptotic thinned Markov moments on inhomogeneous discrete time Markov chains and quantitative and qualitative limits of exponential asymptotics achievement points for chains of birth and death in the series scheme. Semiparametrychna model mixtures with varying concentrations generalized to the case when the parametric model set for multiple component mixtures, and other components necessary to evaluate nonparametric. Retrieved construction of symmetric stochastic integral of a random function with general stochastic measure. The existence and oneness with the given solutions of the integral is given concrete form solutions. We prove the unique solvability of mixed stochastic dyferentsiyalnyh equations with delay. Established integration solution subdivision mixed stochastic differential equations, their regularity in terms Malyavena . Established by the Central extreme theorems for functionals of random fields in terms of spectral densities . Applied Robust regression to assess the Ukraine capital investment , particularly for small areas ( domains). The results of research to the educational process Mechanics and Mathematics, Kyiv National Taras Shevchenko University. Stochastic Differential Equations, multi-fractional stable processes, risk processes, financial models, long-range dependence, statistical estimation. Product Description popup.authors Борисенко О.Д. Голомозий В.В. Зубченко В.П. Карташов М.В. Карташов Ю.М. Кнопова В. Козаченко Ю.В. Королюк Д. Кукуш О.Г. Мішура Ю.С. Майборода Р.Є. Моклячук М.П. Радченко В.М. Ральченко К.В. Сахно Л.М. Шевченко Г.М. Шевчук І.О. Шкляр С.В. Ямненко Р.Є. Яневич Т.О. popup.nrat_date 2020-04-02 Close