A Galton–Watson process with a threshold

Athreya, K. B. ; Schuh, H.-J. (2016) A Galton–Watson process with a threshold Journal of Applied Probability, 53 (2). pp. 614-621. ISSN 0021-9002

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Official URL: http://doi.org/10.1017/jpr.2016.26

Related URL: http://dx.doi.org/10.1017/jpr.2016.26


In this paper we study a special class of size dependent branching processes. We assume that for some positive integer K as long as the population size does not exceed level K, the process evolves as a discrete-time supercritical branching process, and when the population size exceeds level K, it evolves as a subcritical or critical branching process. It is shown that this process does die out in finite time T. The question of when the mean value E(T) is finite or infinite is also addressed.

Item Type:Article
Source:Copyright of this article belongs to Applied Probability Trust
Keywords:Branching process, size dependence, threshold, extinction time
ID Code:131557
Deposited On:07 Dec 2022 05:56
Last Modified:07 Dec 2022 05:56

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