Asymptotic properties of stochastic particle systems with Boltzmann type interaction
- Tribe, Roger
- Wagner, Wolfgang
2010 Mathematics Subject Classification
- 60K35 76P05 82C40
- Interacting particle systems, empirical measures, law of large numbers, co vergence of moments, Boltzmann type equation
We study the asymptotic behaviour of a stochastic particle system that is determined by an independent motion of each particle and by an interadion mechanism between pairs of particles. The limit of the empirical measures of the system is characterized by a nonlinear equation, which is related to the Boltzmann equation. Using a uniqueness result for the limiting equation, we establish a law of large numbers. We also investigate the convergence of moments of the empirical measures.