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Self-similar scaling limits of non-increasing Markov chains

dc.contributor.authorMiermont, Grégory
dc.contributor.authorHaas, Bénédicte
dc.date.accessioned2011-10-13T11:38:13Z
dc.date.available2011-10-13T11:38:13Z
dc.date.issued2011
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/7203
dc.language.isoenen
dc.subjectregular variationen
dc.subjectself-similar Markov processesen
dc.subjectregenerative compositionsen
dc.subjectΛ-coalescentsen
dc.subjectrandom walks with a barrieren
dc.subjectabsorption timeen
dc.subject.ddc519en
dc.titleSelf-similar scaling limits of non-increasing Markov chainsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe study scaling limits of non-increasing Markov chains with values in the set of non-negative integers, under the assumption that the large jump events are rare and happen at rates that behave like a negative power of the current state. We show that the chain starting from n and appropriately rescaled, converges in distribution, as n → ∞, to a non-increasing self-similar Markov process. This convergence holds jointly with that of the rescaled absorption time to the time at which the self-similar Markov process reaches first 0. We discuss various applications to the study of random walks with a barrier, of the number of collisions in Λ-coalescents that do not descend from infinity and of non-consistent regenerative compositions. Further applications to the scaling limits of Markov branching trees are developed in the forthcoming paper [1 1].en
dc.relation.isversionofjnlnameBernoulli
dc.relation.isversionofjnlvol17
dc.relation.isversionofjnlissue4
dc.relation.isversionofjnldate2011
dc.relation.isversionofjnlpages1217-1247
dc.relation.isversionofdoihttp://dx.doi.org/10.3150/10-BEJ312
dc.identifier.urlsitehttp://arxiv.org/abs/0909.3764v1en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherBernoulli Societyen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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