Stochastic dynamics as a limit of Hamiltonian dynamics of hard spheres
We consider the stochastic dynamics that is the Boltzmann-Grad limit of the Hamiltonian dynamics of a system of hard spheres. A new concept of averages over states of stochastic systems is introduced, in which the contribution of the hypersurfaces on which stochastic point particles interact is taken into account. We give a rigorous derivation of the infinitesimal operators of the semigroups of evolution operators.
English version (Springer): Ukrainian Mathematical Journal 51 (1999), no. 5, pp 614-635.
Citation Example: Lampis M., Petrina D. Ya., Petrina К. D. Stochastic dynamics as a limit of Hamiltonian dynamics of hard spheres // Ukr. Mat. Zh. - 1999. - 51, № 5. - pp. 614-635.