A stochastic particle numerical method for 3D Boltzmann equations without cutoff

Using the main ideas of Tanaka, the measure-solution {P_t}_t of a 3-dimensional spatially homogeneous Boltzmann equation of Maxwellian molecules without cutoff is related to a Poisson-driven stochastic differential equation. Using this tool, the convergence to {P_t}_t of solutions {P_t^l}_t of approximating Boltzmann equations with cutoff is proved. Then, a result of Graham-Méléard is used and allows us to approximate {P_t^l}_t with the empirical measure {μ_t^l,n}_t of an easily simulable interacting particle system. Precise rates of convergence are given. A numerical study lies at the end of the paper.