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Information × Registration Number 0217U006743, 0116U002530 , R & D reports Title Investigation and statistical analysis of the asymptotic behavior of complex stochastic nonhomogeneous dynamic systems popup.stage_title Head Mishura Yuliya Stepanivna, Registration Date 18-12-2017 Organization Taras Shevchenko Kiev University popup.description2 The objects of investigation are random processes and fields, financial markets, nonstandard stochastic differential equations, algebraic polynomials. The aims of the work are development of theory of long-memory processes, determination of optimal hedging strategy under long-range dependence, study of properties of random dynamical systems generated by stochastic differential equations, investigation of optimal estimation methods (interpolation, extrapolation) for functionals of unknown values of stochastic processes, estimation in multiple regression models with measurement errors, development of new methods for statistical analysis of efficiency of algorithms for statistics of mixtures. The methods of investigation are analytic methods of probability theory and mathematical statistics, methods of theory of random processes and stochastic analysis, methods of stochastic modelling and optimization theory. Main results of investigation obtained in the work: We prove that it is possible to hedge payment obligations on a long-range market when payment functions are of polynomial growth and may have jump discontinuities. We obtain discrete-time approximations of that market, investigate the rate of convergence of option prices and propose an optimization on the market that leads to a significant reduction of calculation. We obtain a representation of random variables and solve the utility maximization problem in models with long-range dependence. We establish existence and properties of solutions to partial stochastic differential equations with stable distributions of randomness. We propose a new algorithm to model fractional Brownian motion with given reliability and accuracy in Lp(T). We develop the minimum contrast method for estimation of models of random fields with long-range dependence, which are defined by stochastic differential equations with fractional operators; we establish the consistency and asymptotic normality of the corresponding estimators. We prove that in contrast to the piecewise monotonic and piecewise convex approximations, for q>2, a Jackson-type estimate does not hold for the error of approximation of a function by algebraic polynomials that are co-q-monotone with it. We investigate optimal (in mean square sense) linear estimation problems for functionals of harmonized periodically correlated stochastic processes and cointegrable sequences, as well as problems of minimax filtration for functionals of unknown values of stochastic sequences with stationary increments. We investigate the asymptotic behavior of a modification of the Kaplan-Meier estimator for the distribution function of components of a mixture with variable concentrations on the basis of censored data. We find conditions of consistency and asymptotic normality of the corrected least squares estimator for the regression parameter in the polynomial functional model with measurement errors. In the observation model for a Gaussian random process, we establish the form of the maximum likelihood estimator for angular trend coefficient, sufficient conditions for strong consistency of the estimator as observation time increases, sufficient conditions for convergence of estimators based on observations of the random process in finite number of points to the maximum likelihood estimator as the number of observations increases inside a fixed time interval. We propose criteria for hypothesis testing that involves several components at the same time, and similar criteria for hypothesis testing of correlation function in multidimensional case. We introduce bonus-malus systems with different claim types and varying deductibles and study their basic properties. The results of the work have been introduced into the teaching process at the Faculty of Mechanics and Mathematics of Taras Shevchenko National University of Kyiv. Product Description popup.authors Боднарчук І.М. Зубченко В.П. Зутула Д.В. Козаченко Ю.В. Кукуш О.Г. Мішура Ю.С. Майборода Р.Є. Моклячук М.П. Рагуліна О.Ю. Сахно Л.М. Шевченко Г.М. Шевчук І.О. Шкляр С.В. popup.nrat_date 2020-04-02 Close