Some properties of stationary continuous state branching processes

Romain Abraham, Jean-François Delmas and Hui He

Stochastic Processes and their Applications, 2021, vol. 141, issue C, 309-343

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.

Keywords: Continuous state branching process with immigration; Quasi-stationary distribution; Genealogical tree; Ancestral process (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spa.2021.07.011

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