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Information × Registration Number 0212U005420, 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 31-10-2012 Organization Taras Shevchenko Kiev university popup.description2 Object of research is the random processes and fields, stochastic differential equations, financial markets and the processes of risk. The purpose of the work is the studying of the distributions of the behavior of trajectory of processes with complex long-term dependence; the establishing the functional limit theorems for primary and derivative price processes in financial market; the development of approximation methods and statistical analysis of random processes; the development of stochastic models in actuarial mathematics problems. The methods of research is the analytical methods of probability theory and mathematical statistics and stochastic simulation methods. The main research results obtained in the work is the receiving the limit theorems for integrals by semi-martingales to determine the prices of barrier options in the Black-Scholes model with random drift coefficient and volatility. The problem of quantile hedging for models with long-term dependence is solved. The integrals of real functions by the general random measures is studied. This results are applied to solve the stochastic equations with such random measures. The uniform estimation of evaluation function which performs conformal mapping of inside domain with piecewise smooth boundary on the circle is studied. The method of evaluation of Gaussian random processes using wavelet expansions is proposed, the properties of estimates is studied. The harmonized multy-fractional resistant processes and fields are determined, the continuity of their implementations is proved; the existence of local time and there continuity of the totality of variables. The spectral expansion of tensor random fields on the sphere is established. A new variant of calculation of integrals by the Monte-Carlo method and modeling of Cox's processes, which managed by logarithmically Gaussian processes is proposed, the accuracy and reliability of each of these methods are investigated. The consistent semi-parametric estimations for unknown parameters of components in the mixture model with variable concentrations are built. In the Berk model for Poisson regression the sufficient conditions of consistence of estimator of parameter of regression by the quasi-probability method is adduced. The estimations of durability of inhomogeneously perturbed assessment of perturbed equations of recovery is found. These estimates are applied to the risk theory. The estimations of moments of gluing independent discrete processes of recovery are established. The method of maximum bonding for investigating the durability of Markov chains with a uniform and strong mixing. The results of Research Laboratory are implemented in the educational process of Mechanics and Mathematics Faculty National Taras Shevchenko University of Kyiv. Stochastic Differential Equations, multi-fractional standing process, processes of risk, financial models, long-term dependence, statistical estimation. Product Description popup.authors Борисенко О.Д. Дорошенко В.В. Карташов М.В. Карташов Ю.М. Клименко Ю.В. Козаченко Ю.В. Кукуш О.Г. Мішура Ю.С. Майборода Р.Є. Моклячук М.П. Полосьмак О.В. Радченко В.М. Сахно Л.М. Семеновська Н.В. Шевченко Г.М. Шевчук І.О. Шкляр С.В. Ямненко Р.Є. popup.nrat_date 2020-04-02 Close