Stochastic dynamics as a limit of Hamiltonian dynamics of hard spheres

  • M. Lampis
  • D. Ya. Petrina
  • К. D. Petrina


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.
How to Cite
Lampis, M., D. Y. Petrina, and PetrinaК. D. “Stochastic Dynamics As a Limit of Hamiltonian Dynamics of Hard Spheres”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 51, no. 5, May 1999, pp. 614-35,
Research articles