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Information × Registration Number 0209U002765, 0108U003689 , R & D reports Title Asymptotical behaviour of stochastic flows popup.stage_title Head Dorogovtsev Andrey Anatolyevich, Доктор фізико-математичних наук Registration Date 13-03-2009 Organization Institute of mathematics NAS of Ukraine popup.description2 Large deviations principle is proved for a) stochastic flow of interacting particles, b) stochastic differential equations with local time and quickly oscillating coefficients, c) stochastic differential equations with discontinuous coefficients, d) telegraph wave type processes. Square entropy for stochastic flows in a real line is introduced. It is proved that this entropy is finite for any flow of Brownian particles. Finiteness of the average run of all particles of Arratia's flow starting from any finite interval is a corollary of the finiteness of square entropy. Stochastic analogue of Liouville's theorem for infinite-dimensional stochastic flow is proved. Necessary and sufficient conditions connecting ergodic properties for Markov process with locally compact phase space, spectral properties of this process and asymptotic properties of moments of hitting some fixed sets are determined. Product Description popup.authors popup.nrat_date 2020-04-02 Close