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Information × Registration Number 0120U104118, ( 0221U101597  ) R & D request Title Complexity of many-particle stochastic systems Head Konarovskyi Vitalii V., Кандидат фізико-математичних наук Registration Date 01-10-2020 Organization The Institute of Mathematics of NASU popup.description1 The goal of the project is the study of singular stochastic partial differential equations and the study of probabilistic characteristics of interacting particle systems. The description of families of strong random operators that form semigroups with respect to the generalized Wick product in a non-Gaussian case will be obtained. Such a result will generalize the well-known Krylov-Veretennikov expansion and a theorem on a structure of multiplicative functionals from the Gaussian white noise. The problem of recovery of an additive noise from a generated stochastic semigroup will be studied. Obtained theoretical results will be applied to measure-valued processes and flows with singular interaction that appear in models of population genetics and turbulence. Regular modifications of coalescing stochastic flows and stochastic flows of kernels will be constructed, and functionals that describe clusterization in such flows will be investigated. For a number of singular stochastic partial differential equations the existence of non-trivial solutions will be established, their geometric properties will be studied, and the behaviour of these solutions when the driving noise converges to the white noise will be described. popup.nrat_date 2024-12-10 Close