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Information × Registration Number 0212U007447, 0112U006841 , R & D reports Title Dscovering of stochastic dynamics of continuous systems popup.stage_title Head Finkelshtein Dmytro Leonidovych, Registration Date 27-12-2012 Organization Institute of mathematics NAS of Ukraine popup.description2 The connection between convolutions of measures and their correlation functions on configuration spaces is considered. The sufficient conditions for the positive definiteness in the sense of Lenard for the Ruelle convolution on the spaces of finite configurations are found. The properties of derivation operators with respect to the Ruelle convolution are studied, they applied to derive the evolution equations for cummulants of the corresponding probability measures in the dynamics with generators of spatial branching type. The evolutions of correlation functions, which correspond to the Glauber dynamics for continuous systems, in a Banach space of bounded weighted functions are constructed. We consider question about the positive definitness of these correlation functions in the sense of Lenard. We studied ergodic prperties of the corresponding dynamics. We have found the sufficient conditions out the set of small parameters for the existense of Glauber dynamics of Bogolyubov functionals on finite time interval. The convergence of evolution dynamics in Vlasov scaling is proved, the corresponding non-linear non-local kinetic equation is derived and considered. Product Description popup.authors popup.nrat_date 2020-04-02 Close