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Information × Registration Number 0213U000035, 0112U005613 , R & D reports Title Investigation of flows generated by stochastic differential equations with singularities popup.stage_title Head Pilipenko Andrey, Registration Date 14-01-2013 Organization Institute of mathematics NAS of Ukraine popup.description2 In the project questions concerning the behaviour of solutions of stochastic differential equations with singularities are considered. There equations arise as a mathematical model for describing diffusion processes in media with a reflecting boundary or semitransparent membrane and when the behaviour of an infinite system of interacting particles in random media is studied or so on. The joint behaviour of solutions starting from different points is investigated for the corresponding stochastic processes. In particular, generalized differentiability w.r.t. the initial condition for stochastic flows with reflection and those with stable Levy noise, which drift coefficient is just a function of bounded variation, is proved. Also these flows are proved to be flows of homeomorphisms. The asymptotic behaviour for the distance between solutions that have started from different initial points is found. A sequence of limit theorems for random walk with perturbations within neighborhood of zero is obtained. Analogues to the Donsker theorem are found, the limit processes being the skew Brownian motion and the Wiener process with jump-like conditions of conjugation in zero, of Ventsel type. For infinite systems of stochastic equations describing motion of interacting particles in random media the existence of solution theorem is established. A new method of investigation of asymptotic properties of the maximum likelihood estimate in models with discrete observations of the solution of a stochastic differential equation with Levy noise is developed. The idea similar to that of the Trotter formula is used for the Brownian web. Estimates on the Ito-Wiener defor theThe distribution of the number of windings of a planar random field over the curve is investigated. Product Description popup.authors Ізюмцева Ольга Леонідівна Арясова Ольга Вікторівна Вовчанський Микола Богданович Дороговцев Андрій Анатолійович Кузнецов Василь Олексійович Кулик Олексій Михайлович Пилипенко Андрій Юрійович Приходько Юрій Євгенович Руденко Олексій Володимирович Рябов Георгій Валентинович Танцюра Максим Вікторович popup.nrat_date 2020-04-02 Close