DC MetaData pour: A Markov process associated with a Boltzmann equation without cutoff and for non Maxwell molecules


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):

N. FOURNIER

S. MÉLÉARD

Code(s) de Classification MSC:

60J75 Jump processes
60H10 Stochastic ordinary differential equations, See Also {
60K35 Interacting random processes; statistical mechanics type models; percolation theory, See also {82B43, 82C43}
82C40 Kinetic theory of gases

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