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Pré-Publication, Document De Travail Année : 2022

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

Résumé

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.
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Dates et versions

hal-03854678 , version 1 (16-11-2022)

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  • HAL Id : hal-03854678 , version 1

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Simon C Harris, Emma Horton, Andreas E Kyprianou, Ellen Powell. Many-to-few for non-local branching Markov process. 2022. ⟨hal-03854678⟩
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