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:**

- 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:** 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