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A new approach to quantitative propagation of chaos for drift, diffusion and jump processes

Wennberg, Bernt; Mouhot, Clément; Mischler, Stéphane (2015), A new approach to quantitative propagation of chaos for drift, diffusion and jump processes, Probability Theory and Related Fields, 161, 1-2, p. 1-59. http://dx.doi.org/10.1007/s00440-013-0542-8

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00559132/fr/
Date
2015
Journal name
Probability Theory and Related Fields
Volume
161
Number
1-2
Publisher
Springer
Pages
1-59
Publication identifier
http://dx.doi.org/10.1007/s00440-013-0542-8
Metadata
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Author(s)
Wennberg, Bernt
Mouhot, Clément
Mischler, Stéphane
Abstract (EN)
This paper is devoted the the study of the mean-field limit for many-particle systems undergoing jump, drift or diffusion processes, as well as combinations of them. The main results are quantitative estimates on the decay of fluctuations around the deterministic limit and of correlations between particles, as the number of particles goes to infinity. To this end we introduce a general functional framework which reduces this question to the one of proving a purely functional estimate on some abstract generator operators (consistency estimate) together with fine stability estimates on the flow of the limiting non-linear equation (stability estimates). Then we apply this method to a Boltzmann collision jump process (for Maxwell molecules), to a McKean-Vlasov drift-diffusion process and to an inelastic Boltzmann collision jump process with (stochastic) thermal bath. To our knowledge, our approach yields the first such quantitative results for a combination of jump and diffusion processes.
Subjects / Keywords
granular gas; inelastic collision; drift-diffusion; McKean-Vlasov equation; Boltzmann equation; fluctuations; quantitative; mean-field limit

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