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dc.contributor.authorMischler, Stéphane
dc.contributor.authorTristani, Isabelle
dc.date.accessioned2017-12-01T10:29:25Z
dc.date.available2017-12-01T10:29:25Z
dc.date.issued2015
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17137
dc.language.isoenen
dc.subjectsemigroup
dc.subjectdissipativity
dc.subjectFokker-Planck equation
dc.subjectfractional Laplacian
dc.subjectspectral gap
dc.subjectexponential rate of convergence
dc.subjectlong-time asymptotic
dc.subject.ddc515en
dc.titleUniform semigroup spectral analysis of the discrete, fractional & classical Fokker-Planck equations
dc.typeDocument de travail / Working paper
dc.description.abstractenIn this paper, we investigate the spectral analysis (from the point of view of semi-groups) of discrete, fractional and classical Fokker-Planck equations. Discrete and fractional Fokker-Planck equations converge in some sense to the classical one. As a consequence, we first deal with discrete and classical Fokker-Planck equations in a same framework, proving uniform spectral estimates using a perturbation argument and an enlargement argument. Then, we do a similar analysis for fractional and classical Fokker-Planck equations using an argument of enlargement of the space in which the semigroup decays. We also handle another class of discrete Fokker-Planck equations which converge to the fractional Fokker-Planck one, we are also able to treat these equations in a same framework from the spectral analysis viewpoint, still with a semigroup approach and thanks to a perturbative argument combined with an enlargement one. Let us emphasize here that we improve the perturbative argument introduced in [7] and developed in [11], relaxing the hypothesis of the theorem, enlarging thus the class of operators which fulfills the assumptions required to apply it.
dc.identifier.citationpages45
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris-Dauphine
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01177101
dc.subject.ddclabelAnalyseen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.date.updated2017-12-20T15:04:58Z
hal.person.labIds60
hal.person.labIds18


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