REMAINING-LIFETIME AGE-STRUCTURED BRANCHING PROCESSES

doi:10.1007/s10473-025-0319-z

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (3): 1107-1136.doi: 10.1007/s10473-025-0319-z

REMAINING-LIFETIME AGE-STRUCTURED BRANCHING PROCESSES

Ziling CHENG^†, Zenghu LI

School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

收稿日期:2023-08-02 修回日期:2023-12-14 出版日期:2025-05-25 发布日期:2025-09-30

REMAINING-LIFETIME AGE-STRUCTURED BRANCHING PROCESSES

Ziling CHENG^†, Zenghu LI

School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

Received:2023-08-02 Revised:2023-12-14 Online:2025-05-25 Published:2025-09-30
Contact: ^†Ziling CHENG, E-mail: zlcheng@mail.bnu.edu.cn
About author:Zenghu LI, E-mail: lizh@bnu.edu.cn
Supported by:
National Key R&D Program of China (2020YFA0712901).

摘要/Abstract

摘要： 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.

关键词: branching process, remaining lifetime, immigration, stochastic equation, ergodicity, occupation time, large number law, central limit theorem

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.

Key words: branching process, remaining lifetime, immigration, stochastic equation, ergodicity, occupation time, large number law, central limit theorem

中图分类号:

60J80

Ziling CHENG, Zenghu LI. REMAINING-LIFETIME AGE-STRUCTURED BRANCHING PROCESSES[J]. 数学物理学报(英文版), 2025, 45(3): 1107-1136.

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

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REMAINING-LIFETIME AGE-STRUCTURED BRANCHING PROCESSES

REMAINING-LIFETIME AGE-STRUCTURED BRANCHING PROCESSES

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