HARRIS, Simon; HORTON, Emma; KYPRIANOU, Andreas; POWELL, Ellen

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HARRIS, Simon
Department of Statistics [Auckland]

HORTON, Emma
Méthodes avancées d’apprentissage statistique et de contrôle [ASTRAL]

KYPRIANOU, Andreas
Department of Mathematical Sciences [Bath]

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We 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.< Réduire

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non-local branching processes

many-to-few

spines

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Many-to-few for non-local branching Markov process

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Résumé en anglais

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