REMAINING-LIFETIME AGE-STRUCTURED BRANCHING PROCESSES

  • Ziling CHENG ,
  • Zenghu LI
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  • School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
Zenghu LI, E-mail: lizh@bnu.edu.cn

Received date: 2023-08-02

  Revised date: 2023-12-14

  Online published: 2025-09-30

Supported by

National Key R&D Program of China (2020YFA0712901).

Abstract

We study age-structured branching models with reproduction law depending on the remaining lifetime of the parent. The lifespan of an individual is determined at its birth and its remaining lifetime decreases at the unit speed. The models, without or with immigration, are constructed as measure-valued processes by pathwise unique solutions of stochastic equations driven by time-space Poisson random measures. In the subcritical branching case, we give a sufficient condition for the ergodicity of the process with immigration. Two large number laws and a central limit theorem of the occupation times are proved.

Cite this article

Ziling CHENG , Zenghu LI . REMAINING-LIFETIME AGE-STRUCTURED BRANCHING PROCESSES[J]. Acta mathematica scientia, Series B, 2025 , 45(3) : 1107 -1136 . DOI: 10.1007/s10473-025-0319-z

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