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

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

Monte-Carlo approximations and fluctuations for 2D Boltzmann equations without cutoff


Code(s) de Classification MSC:

Résumé: Using the main ideas of Tanaka, the measure solution $\{P_t\}_t$ of a $2$-dimensional spatially homogeneous Boltzmann equation of Maxwellian molecules without cutoff is related to a Poisson-driven nonlinear stochastic differential equation. Using this tool and a generalized law of large numbers, we present two ways to prove the convergence of the empirical measure associated with an interacting particle system to this measure solution of the Boltzmann equation. Then we give numerical results. We finally discuss about a central limit theorem associated with the above law of large numbers.

Mots Clés: Boltzmann equations without cutoff ; Stochastic differential equations ; Jump measures ; Interacting particle systems ; Fluctuation theorems

Date: 2000-06-16

Prépublication numéro: PMA-601

Postscript file :PMA-601.ps