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:** 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