Strict positivity of the solution to a 2-dimensional spatially homogeneous Boltzmann equation without cutoff

ABSTRACT. – We consider a 2-dimensional spatially homogeneous Boltzmann equation without cutoff, which we relate to a Poisson driven nonlinear S.D.E. We know from [8] that this S.D.E. admits a solution Vt, and that for each t> 0, the law of Vt admits a density f (t,.). This density satisfies the Boltzmann equation. We use here the stochastic calculus of variations for Poisson functionals, in order to prove that f does never vanish. 2001 Éditions scientifiques et médicales Elsevier SA