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

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 60H07 Stochastic calculus of variations and the Malliavin calculus
- 82C40 Kinetic theory of gases
- 35B65 Smoothness/regularity of solutions of PDE

**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*