Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

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

Auteur(s):

Code(s) de Classification MSC:

Résumé: 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 a previous work that this S.D.E. admits a solution $V_t$, and that for each $t>0$, the law of $V_t$ 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.

Mots Clés: Boltzmann equation without cutoff ; Poisson measure ; Stochastic calculus of variations

Date: 1999-12-08

Prépublication numéro: PMA-546