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

dc.contributor.authorWennberg, Bernt
dc.contributor.authorMouhot, Clément
HAL ID: 1892
dc.contributor.authorMischler, Stéphane
dc.date.accessioned2011-02-07T16:05:47Z
dc.date.available2011-02-07T16:05:47Z
dc.date.issued2015
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/5675
dc.language.isoenen
dc.subjectgranular gasen
dc.subjectinelastic collisionen
dc.subjectdrift-diffusionen
dc.subjectMcKean-Vlasov equationen
dc.subjectBoltzmann equationen
dc.subjectfluctuationsen
dc.subjectquantitativeen
dc.subjectmean-field limiten
dc.subject.ddc519en
dc.titleA new approach to quantitative propagation of chaos for drift, diffusion and jump processesen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherDepartment of Mathematical Sciences Chalmers University of Technology – University of Gothenburg;Suède
dc.contributor.editoruniversityotherDPMMS/CMS University of Cambridge;Royaume-Uni
dc.description.abstractenThis 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.en
dc.relation.isversionofjnlnameProbability Theory and Related Fields
dc.relation.isversionofjnlvol161
dc.relation.isversionofjnlissue1-2
dc.relation.isversionofjnldate2015
dc.relation.isversionofjnlpages1-59
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/s00440-013-0542-8
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00559132/fr/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSpringer
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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