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Pré-publication, Document de travail

Some Properties of Stationary Continuos State Branching Processes

Abstract : We consider the genealogical tree of a stationary continuous state branching process with immigration. For a sub-critical stable branching mechanism, we consider the genealogical tree of the extant population at some fixed time and prove that, up to a deterministic time-change, it is distributed as a continuous-time Galton-Watson process with immigration. We obtain similar results for a critical stable branching mechanism when only looking at immigrants arriving in some fixed time-interval. For a general sub-critical branching mechanism, we consider the number of individuals that give descendants in the extant population. The associated processes (forward or backward in time) are pure-death or pure-birth Markov processes, for which we compute the transition rates.
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Pré-publication, Document de travail
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https://hal.archives-ouvertes.fr/hal-02614083
Contributeur : Romain Abraham <>
Soumis le : mercredi 20 mai 2020 - 16:14:41
Dernière modification le : jeudi 11 juin 2020 - 03:59:00

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  • HAL Id : hal-02614083, version 1

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Romain Abraham, Jean-François Delmas, Hui He. Some Properties of Stationary Continuos State Branching Processes. 2020. ⟨hal-02614083⟩

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