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Information × Registration Number 0219U003400, 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 11-02-2019 Organization Taras Shevchenko Kiev University popup.description2 The objects of investigation are random processes and fields, financial markets, stochastic differential equations, integral metrics, multiple regression models. The aims of the work are development of the theory of mixed fractional and multifractional processes, establishing limit theorems for financial markets, determination of optimal hedging strategy, study of properties of random dynamical systems, investigation of optimal estimation methods for functionals of unknown values of stochastic processes, development of new methods for statistical analysis of efficiency of statistical algorithms. The methods of investigation are analytic methods of probability theory and mathematical statistics, methods of stochastic analysis, modelling, optimization theory and new statistical methods. Main results of investigation obtained in the work: We construct statistical estimators of unknown parameters in mixed long- and short-memory models as well as in fractional and multifractional models. We propose new methods for hypothesis testing of the drift parameter sign of fractional processes. We prove the regularity of local times for square-Gaussian processes. We establish properties of generalized solutions to partial stochastic differential equations with stable noise. We construct an integral with respect to the measure driven by a fractional stable field. We obtain convergence conditions and rate for random processes from Orlicz spaces and other special spaces. We propose a new algorithm to model a fractional Brownian motion with given reliability and accuracy in Lp([0,T]). We construct a new smoothness scale for differentiable functions, develop new methods to approximate functions in integral metrics and find bounds for monotone approximation errors with Jacobi weight. We investigate estimation problems (interpolation, extrapolation) for functionals of unknown values of harmonized stochastic processes on the basis of observations with missing values. We develop modified and new algorithms for regression analysis as well as survival analysis in nonparametric mixture models. We construct a modification of the Kaplan-Meier estimator for a mixture with variable concentrations. We prove that a comonotone distribution of a stock price is possible provided that there are deterministic relations in the stock price dynamics. We obtain simplified conditions for consistency and asymptotic normality of the estimator in the polynomial model. We construct consistence estimators in nonlinear multiple regression models with errors of different types. We conduct a comparative analysis of cohort estimates and estimates in a case control study scheme. For the Cox proportional-hazards model, we construct strongly consistent joint estimators for the basic risk function and regression parameters as well as a fitting criterion. We prove new central limit theorems for spectral functionals of random fields and apply them to problems of statistical estimation in a spectral domain. We establish governing equations in terms of differential-convolution operators for distributions of generalized Poisson processes. We estimate large deviation probabilities for processes from different functional spaces. We propose new criteria to test hypotheses about the covariance function and spectra. We find the rate of convergence of prices for financial assets with jumps and strong dependence. We introduce and investigate a symmetric integral of a random function with respect to a general stochastic measure. We develop practical approaches to the ruin probability estimation, investigate a generalization of the risk model with stochastic premiums and bonus-malus systems with different claim types. 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. Моклячук Т.О. Рагуліна О.Ю. Сахно Л.М. Шевченко Г.М. Шевчук І.О. Шкляр С.В. popup.nrat_date 2020-04-02 Close