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Information × Registration Number 0213U003608, 0112U005134 , R & D reports Title Stochastic flows with singular interaction popup.stage_title Head Dorogovtsev Andrii Anatoliyovych, Доктор фізико-математичних наук Registration Date 08-02-2013 Organization Institute of mathematics NAS of Ukraine popup.description2 The project is devoted to the study of asymptotic properties of stochastic flows with singular interaction. The study of such processes is an important problem of modern theory of stochastic processes, because stochastic flows with singular interaction are used to model a number of physical processes. It is not possible to use well developed apparatus from the theory of flows of diffeomorphisms to solve such problems. In proprosed problems question about mathematical modelling of flows with singular interactions is studied, asymptotic behaviour of single trajectory of such flows as well as the whole flow as a measure-valued process is investigated, stochastic semigroups of operators which are defined by such flows are studied. Main results are following. 1) Asymptotic expansion of a neighborhood of a trajectory of compactly perturbed Wiener process is obtained. 2) Integral representation of general multiplicative family of operators, which describe inhomogeneous Feller process obtained via pasting together two difuusion processes is obtained. 3) Theorems of duffision approximation type for models with Markov perturbations with non-uniform estimates on the speed of convergence of transition probabilities to unique invariant distribution are proved. 4) The question about existence of gluing in stochastic flows generated by SDE with discontinuous coefficients is studied. 5) Existence of infinite system of heavy diffusion particles sticking together at the meeting moment is stated. 6) Approximation of finite dimensional distribution of Arratia flow by finite dimensional distribution of flows generated by SDE is constructed. 7) The structure of orthogonal polynomials with respect to singular transformations of Gaussian measure is studied. Product Description popup.authors Ізюмцева Ольга Леонідівна Конаровський Віталій Васильович Копитко Богдан Іванович Кулик Олексій Михайлович Махно Сергій Якович Пилипенко Андрій Юрійович Рябов Георгій Валентинович Шевчук Роман Володимирович popup.nrat_date 2020-04-02 Close