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

Using the main ideas of Tanaka, the measure-solution {Pt}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 {Pt}t of solutions {P l t}t of approximating Boltzmann equations with cutoff is proved. Then, a result of Graham-Méléard is used and allows us to approximate {P l t}t with the empirical measure {μ t }t of an easily simulable interacting particle system. Precise rates of convergence are given. A numerical study lies at the end of the paper.