A Markov process associated with a Boltzmann equation without cutoff and for non-Maxwell molecules

Tanaka,((18)) showed a way to relate the measure solution {P-t}(t) of a spa tially homogeneous Boltzmann equation of Maxwellian molecules without angul ar cutoff to a Poisson-driven stochastic differential equation: {P-t} is th e flow of time marginals of the solution of this stochastic equation. In th e present paper, we extend this probabilistic interpretation to much more g eneral spatially homogeneous Boltzmann equations. Then we derive from this interpretation a numerical method for the concerned Boltzmann equations, by using easily simulable interacting particle systems.