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

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

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

Auteur(s):

Code(s) de Classification MSC:

Résumé: Tanaka \cite{Tanaka:78}, showed a way to relate the measure solution $\{P_t\}_t$ of a spatially homogeneous Boltzmann equation of Maxwellian molecules without angular cutoff to a Poisson-driven stochastic differential equation: $\{P_t\}$ is the flow of time marginals of the solution of this stochastic equation.\\ In the present paper, we extend this probabilistic interpretation to much more general 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.

Mots Clés: Boltzmann equations without cutoff ; Nonlinear stochastic differential equations ; Jump measures ; Interacting particle systems

Date: 2000-09-06

Prépublication numéro: PMA-608

Postscript file : PMA-608.ps