| Université Paris 6 Pierre et Marie Curie | Université Paris 7 Denis Diderot | |
| CNRS U.M.R. 7599 | ||
| ``Probabilités et Modèles Aléatoires'' | ||
Auteur(s):
Code(s) de Classification MSC:
Résumé: Using the main ideas of Tanaka \cite{Tanaka:78}, the measure solution $\{P_t\}_t$ of a $3$-dimensional spatially homogeneous Boltzmann equation of Maxwellian molecules without cutoff is related to a Poisson-driven stochastic differential equation. Using this tool, the convergence to $\{P_t\}_t$ of solutions $\{P^l_t\}_t$ of approximating Boltzmann equations with cutoff is proved. Then, a result of Graham-M\'el\'eard, \cite{Graham:96} is used, and allows to approximate $\{P^l_t\}_t$ with the empirical measure $\{\mu^{l,n}_t\}_t$ of an easily simulable interacting particle system. Precise rates of convergence are given. A numerical study lies at the end of the paper.
Mots Clés: Boltzmann equations without cutoff ; Stochastic differential
equations ; Jump measures ; Interacting particle systems
Date: 2000-02-03
Prépublication numéro: PMA-563
Postscript file : PMA-563.ps
Compressed (gzip) postscript file :
PMA-563.ps.gz