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Information × Registration Number 0216U001718, 0114U002965 , R & D reports Title Geometric aspects of the theory of infinite dimensional dynamical systems popup.stage_title Head Dorogovtsev Andrey Anatolievich, Доктор фізико-математичних наук Registration Date 28-03-2016 Organization Institute of mathematics NAS of Ukraine popup.description2 Stochastic flows with singular interaction is a mathematical model of turbulent flows of a liquid or a gase. An understanding of a geometry of a flow gives a possibility to construct new quantitative characteristics of turbulence and to study their behaviour on big intervals of time. As for now, a general theory that unifies obtained results on a geometry of such systems is absent. In the present research stochastic analogues of differential and topological characteristics of differentiable non-random dynamical systems are built; the existence of local times and self-intersection local times for Gaussian processes, obtained via the action of a second quantization operator on a Wiener process, is proved; an integral representation of a two-parametric operator semigroup, that describes a Feller process on the real line, built via pasting together a finite number of diffusions, is obtained; a new method of proving the local asymptotic normality in statistical models, based on discrete observations of solutions of stochastic differential equations driven by Levy noise, is proposed; an invariance principle for random walks on the real line with non-integrable perturbation at zero is proved; existence and uniqueness of a solution to the stochastic differential equation with Levy noise and discontinuous dirft is proved; existence of local times to solutions of stochastic differential equations with a uniform ellipticity replaced by a Hormander condition is proved; an Ito-Wiener expansion for square integrable functionals from the n-point motion of the Arratia flow is built; non-existence of triple collision points for Harris net is proved. Product Description popup.authors Ізюмцева Ольга Леонідівна Вовчанський Микола Богданович Глиняна Катерина Валеріївна Дороговцев Андрій Анатолійович Копитко Богдан Іванович Кузнецов Василь Олексійович Кулик Олексій Михайлович Махно Сергій Якович Мельник Сергій Анатолійович Пилипенко Андрій Юрійович Руденко Олексій Володимирович Рябов Георгій Валентинович Шевчук Роман Володимирович popup.nrat_date 2020-04-02 Close