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:**

- 60H30 Applications of stochastic analysis (to PDE, etc.)
- 60K35 Interacting random processes; statistical mechanics type models; percolation theory, See also {82B43, 82C43}
- 82C40 Kinetic theory of gases

**Résumé:** In [10], using a typically probabilistic
substitution in the Boltzmann equation, we extend Tanaka's
probabilistic interpretation [19] to much more general spatially
homogeneous Boltzmann equations, i.e. homogeneous Boltzmann equations
without cutoff and for non Maxwell molecules.
In this paper we show how this
interpretation allows us to build some approximating cutoff
interacting particle systems, and to derive some Monte-Carlo
algorithms for the simulation of solutions of the Boltzmann equation.

**Mots Clés:** *Boltzmann equations without cutoff and for non Maxwell molecules ; Nonlinear
stochastic differential equations ; Interacting particle systems ;
Monte-Carlo algorithm*

**Date:** 2000-12-13

**Prépublication numéro:** *PMA-630*

**Postscript file : **PMA-630.ps