A functional law of large numbers for Boltzmann type stochastic particle systems

A large system of particles is studied. Its time evolution is determined as the superposition of two components. The first component is the independent motion of each particle. The second component is the random interaction mechanism between pairs of particles. The intensity of the interaction depends on the state of the system and is assumed to be bounded. Convergence of the empirical measures is proved as the number of particles tends to infinity. The limiting deterministic measure-valued function is characterized as the unique solution of a nonlinear equation of the Boltzmann type