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Construction of age-structured branching processes by stochastic equations

Part of: Markov processes Stochastic analysis

Published online by Cambridge University Press:  31 May 2022

Lina Ji Open the ORCID record for Lina Ji [Opens in a new window]  and
Zenghu Li
Lina Ji*
Affiliation:
Shenzhen MSU-BIT University
Zenghu Li*
Affiliation:
Beijing Normal University
*
*Postal address: Faculty of Computational Mathematics and Cybernetics, Shenzhen MSU-BIT University, Shenzhen 518172, People’s Republic of China. Email: jiln@smbu.edu.cn
**Postal address: Laboratory of Mathematics and Complex Systems, School of Mathematical Sciences, Beijing Normal University, Beijing 100875, People’s Republic of China. Email: lizh@bnu.edu.cn
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Abstract

We provide constructions of age-structured branching processes without or with immigration as pathwise-unique solutions to stochastic integral equations. A necessary and sufficient condition for the ergodicity of the model with immigration is also given.

Keywords

Distribution-function-valued processergodicitymeasure-valuednon-localimmigration

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60J85: Applications of branching processes 60H15: Stochastic partial differential equations
Type
Original Article
Information
Journal of Applied Probability , Volume 59 , Issue 3 , September 2022 , pp. 670 - 684
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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