Binary jumps in continuum. II. Non-equilibrium process and a Vlasov-type   scaling limit
  Let $\Gamma$ denote the space of all locally finite subsets (configurations) in $\mathbb R^d$. A stochastic dynamics of binary jumps in continuum is a Markov process on $\Gamma$ in which pairs of particles simultaneously hop over $\mathbb R^d$. We discuss a non-equilibrium dynamics of binary jumps. We prove the existence of an evolution of correlation functions on a finite time interval. We also show that a Vlasov-type mesoscopic scaling for such a dynamics leads to a generalized Boltzmann non-linear equation for the particle density. 
Dmitri Finkelshtein, Yuri Kondratiev, Oleksandr Kutoviy, Eugene   Lytvynov
math.PR