Limit theorems for a critical branching process with immigration at zero in a random environment

Yinxuan Zhao and Mei Zhang

Statistics & Probability Letters, 2025, vol. 224, issue C

Abstract: In this paper, we study a critical branching process with immigration at zero in a random environment Z, where the immigration is allowed entering a generation iff the previous generation is empty. Firstly, we analyze the asymptotic behavior of the survival probability at generation n of Z̃, a critical branching process in a random environment with random initial number of particles. Then, the convergence rate of the transition probabilities pk,0(n) (k≥0) of Z are obtained, which can be compared with the corresponding results for non-random case in literatures.

Keywords: Branching process; Immigration; Random environment; State dependent; Critical; Transition probabilities (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spl.2025.110435

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