ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

12. Probability and Statistics

1991 MS Classification: 60, 82, 65 Wagner, Wolfgang, Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany Stochastic particle systems approximating the stationary Boltzmann equation We consider a stochastic n-particle system in a bounded domain with diffusive boundary conditions. We study the distance between the stationary measure for the particle system and the measure given by the n-fold product of the solution to the regularized stationary Boltzmann equation with the same boundary conditions. We show that, if the mean free path inverse is sufficiently small, the L_{1}-difference between the k-particle distribution functions of such two measures vanishes in the limit n → ∞, for any fixed k , with the order \frac{1}{n} . Reference: S. Caprino, M. Pulvirenti, and W. Wagner, “Stationary particle systems approximating stationary solutions to the Boltzmann equation”, SIAM J. Math. Anal. (1998). To appear.