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Registration Number

0213U000752, 0111U006561 , R & D reports

Title

Evolutionary systems: analytical study of transformations by the random fluctuation and statistical regularities

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Head

Mishura Yuliya Stepanivna,

Registration Date

15-03-2013

Organization

Taras Shevchenko Kiev university

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Object of research is the random processes and fields, stochastic differential equations, financial markets and risk processes. The purpose of the work is investigation of distributions of functionals of random processes; the development of methods for studying the asymptotic behavior of stopping times in diffusion models; strong approximation of stochastic differential equations with long memory; simulation of random processes; the development of new methods for estimation of parameters of evolution systems; the development of stochastic models in problems of actuarial mathematics. The methods of research are the analytical methods of probability theory and mathematical statistics and stochastic simulation methods. The main research results of the work are: Limit theorems for optimal stopping times in the diffusion model are obtained. The properties of the minimum weighted 4-designs with 10 points on the sphere are studied. The stochastic heat equation with random effect defined by integral over general stochastic measure is investigated. The conditions of stability of Markov chains are proposed. Weak solution of the stochastic parabolic equation with random effects defined by the integral over general stochastic measure is received. The rate of convergence of wavelet expansions of generalized random processes is obtained. The results on existence, uniqueness and convergence of solutions of mixed stochastic differential equations driven by Brownian and fractional Brownian motion are obtained. The application of the averaging method for oscillatory systems in cases where the unperturbed system has stable harmonic oscillations is found. Properties of solutions of stochastic differential equations with random coefficients, non-Lipschitz diffusion and Poisson measures are studied. Algorithms for the best approximation of fractional Brownian motion by Gaussian martingales are proposed. Estimates for the risk function and regression parameter in the Cox model of proportional hazards with errors of regressor measurement are found. The properties of various valuation functions at different sampling designs on the example of the state statistical monitoring of capital investments are investigated. The test for checking the equality of moments of two component of mixture with varying concentrations is constructed, the asymptotic behavior of the test statistics is studied. The problem of minimax estimation of linear functionals of unknown values of periodically correlated stochastic process is solved. The results of Research Laboratory are implemented in the educational process of Mechanics and Mathematics Faculty of Kyiv National Taras Shevchenko University. Stochastic Differential Equations, multi-fractional stable processes, risk processes, financial models, long-range dependence, statistical estimation.

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Борисенко О.Д.
Голомозий В.В.
Дорошенко В.В.
Зубченко В.П.
Карташов М.В.
Карташов Ю.М.
Клименко Ю.В.
Козаченко Ю.В.
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.

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2020-04-02