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Information × Registration Number 0221U101597, 0120U104118 , R & D reports Title Complexity of many-particle stochastic systems popup.stage_title Head Konarovskyi Vitalii V., Кандидат фізико-математичних наук Registration Date 22-01-2021 Organization The Institute of Mathematics of NASU popup.description2  Object of investigation - singular stochastic differential equations with partial derivatives and systems of interacting particles. Aim of the work - study of properties of solutions of stochastic differential equations with singular coefficients, construction of stochastic flows with singular interaction and study of local properties of their trajectories. Methods of investigation - construction of measure-valued solutions of singular stochastic differential equations with partial derivatives via an approximation by finite systems of interacting particles; study of asymptotic behaviour of functionals that characterize the joint motion of particles in the flow by methods of stochastic processes and stochastic analysis; study of finite dimensional Euclidean spaces with geodesic distance defined by a system of vector fields. Stationary stichastic flows of interacting Brownian particles are studied. Limit theorems for integral functionals from a point process generated by the Arratia flow are proved. Sufficient conditions for the existence of regular modifications of coalescing stochastic flows on metric graphs are found. Conditions for the existence of the solution to a sticky reflected stochastic heat equation with Dirichlet boundary conditions are obtained. Sufficient conditions for the existence of self-intersection local times for independent Brownain motions on a Carnot group are established. Obtained results will be applied to the study of semigroups of strong random operators in a non-Gaussian setting, existence of a stationary solution to the sticky reflected stochastic heat equation with Dirichlet boundary conditions and construction of corresponding invariant measure, study of trajectories of Brownian motions on Lie groups. Product Description popup.authors Hlyniana Kateryna V Dorohovtsev Andrii A. Rudenko Oleksii V Riabov Georgii V popup.nrat_date 2021-01-22 Close