Expansion of the propagation of chaos for Bird and Nanbu systems

Details Expansion of the propagation of chaos for Bird and Nanbu systems Expansion of the propagation of chaos for Bird and Nanbu systems

2009-01-22

arxiv.org/abs/0901.3476v8

Mathematics

Probability

Scientific paper

The Bird and Nanbu systems are particle systems used to approximate the solution of the mollied Boltzmann equation. In particular, they have the propagation of chaos property. Following [GM94, GM97, GM99], we use coupling techniques and results on branching processes to write an expansion of the error in the propagation of chaos in terms of the number of particles, for slightly more general systems than the ones cited above. This result leads to the proof of the a.s convergence and the centrallimit theorem for these systems. In particular, we have a central-limit theorem for the empirical measure of the system under less assumptions then in [M\'el98]. As in [GM94, GM97, GM99], these results apply to the trajectories of particles on an interval [0; T].

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