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Information × Registration Number 0216U001717, 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 In the present research stochastic analogues of differential and topological characteristics of differentiable non-random dynamical systems are built. New methods of investigation spatially discontinuous maps that constitute a stochastic flow with singular interaction are developed. A structure of noise that corresponds to singular stochastic flow is studied. An asymptotics of disorder in a discrete flow that approximate the Arratia flow is found. An asymptotic behaviour of joint widing angles of particles in isotropic Brownian stochastic flow is studied. An existence and uniqueness theorem for strong solution of a countable family of stochastic differential equations that describe a motion of interacting particles in a random media is proved. An existence and uniqueness theorem for solutions of stochastic differential equations with Levy noise and discontinuous drift is proved. A comparison theorem for solution of Cauchy problem for stochastic differential equations of parabolic type with non-Lipschitz coefficients. For stochastic differential equations with smooth coefficients that don't satisfy strict ellipticity upper bounds on a transition density of solutions are obtained and existence of a local time 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