A scaling limit of controlled branching processes

Jiawei Liu

Statistics & Probability Letters, 2024, vol. 208, issue C

Abstract: In this paper, a special sequence of controlled branching processes is considered. Using a martingale problem approach, we prove that under some mild conditions the limit of such processes is a kind of continuous branching process with dependent immigration constructed in Li (2019). The conditions are given in terms of probability generating functions and can be realized.

Keywords: Scaling limit; Galton–Watson processes; Random controlled branching processes; Tightness; Weak convergence (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spl.2024.110081

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