Some properties of stationary continuous state branching processes

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:141

Article

Abraham, Romain¹  Delmas, Jean-Francois²  He, Hui³ 

[1] Univ Orleans, Univ Tours, Inst Denis Poisson, CNRS, Orleans, France

[2] Ecole Ponts, CERMICS, Champs Sur Marne, France

[3] Beijing Normal Univ, Sch Math Sci, Beijing, Peoples R China

关键词: Continuous state branching process with immigration;    Quasi-stationary distribution;    Genealogical tree;    Ancestral process;   

DOI  :  10.1016/j.spa.2021.07.011

来源: Elsevier

【 摘 要 】

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 subcritical 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. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free