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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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https://hal.archives-ouvertes.fr/hal-02614083
Contributor : Romain Abraham <>
Submitted on : Wednesday, May 20, 2020 - 4:14:41 PM
Last modification on : Monday, May 25, 2020 - 2:43:55 PM

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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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