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hal.structure.identifierDepartment of Statistics [Auckland]
dc.contributor.authorHARRIS, Simon
hal.structure.identifierMéthodes avancées d’apprentissage statistique et de contrôle [ASTRAL]
dc.contributor.authorHORTON, Emma
hal.structure.identifierDepartment of Mathematical Sciences [Bath]
dc.contributor.authorKYPRIANOU, Andreas
hal.structure.identifierDepartment of Mathematical Sciences [Durham University]
hal.structure.identifierMéthodes avancées d’apprentissage statistique et de contrôle [ASTRAL]
dc.contributor.authorPOWELL, Ellen
dc.date.accessioned2024-04-04T02:39:14Z
dc.date.available2024-04-04T02:39:14Z
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190954
dc.description.abstractEnWe provide a many-to-few formula in the general setting of non-local branching Markov processes. This formula allows one to compute expectations of k-fold sums over functions of the population at k different times. The result generalises [14] to the non-local setting, as introduced in [11] and [8]. As an application, we consider the case when the branching process is critical, and conditioned to survive for a large time. In this setting, we prove a general formula for the limiting law of the death time of the most recent common ancestor of two particles selected uniformly from the population at two different times, as t → ∞. Moreover, we describe the limiting law of the population sizes at two different times, in the same asymptotic regime.
dc.language.isoen
dc.subject.ennon-local branching processes
dc.subject.enmany-to-few
dc.subject.enspines
dc.title.enMany-to-few for non-local branching Markov process
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Probabilités [math.PR]
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-03854678
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03854678v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=HARRIS,%20Simon&HORTON,%20Emma&KYPRIANOU,%20Andreas&POWELL,%20Ellen&rft.genre=preprint


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