1. Some properties of stationary continuous state branching processes.
- Author
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Abraham, Romain, Delmas, Jean-François, and He, Hui
- Subjects
- *
BRANCHING processes , *MARKOV processes , *EMIGRATION & immigration - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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