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Journal Articles Stochastic Processes and their Applications Year : 2021

Some Properties of Stationary Continuous 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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Dates and versions

hal-02614083 , version 1 (20-05-2020)

Identifiers

  • HAL Id : hal-02614083 , version 1

Cite

Romain Abraham, Jean-François Delmas, Hui He. Some Properties of Stationary Continuous State Branching Processes. Stochastic Processes and their Applications, 2021, 141, pp.309-343. ⟨hal-02614083⟩
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