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

We consider a 2-dimensional spatially homogeneous Boltzmann equation withou t cutoff, which we relate to a Poisson driven nonlinear S.D.E. We know from [8] that this S.D.E. admits a solution V-t, and that for each t > 0, the l aw of V-t admits a density f(t,.). This density satisfies the Boltzmann equ ation. We use here the stochastic calculus of variations for Poisson functi onals, in order to prove that S does never vanish. (C) 2001 Editions scient ifiques et medicales Elsevier SAS.