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Linking population-size-dependent and controlled branching processes

Author

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  • Braunsteins, Peter
  • Hautphenne, Sophie
  • Kerlidis, James

Abstract

Population-size dependent branching processes (PSDBPs) and controlled branching processes (CBPs) are two classes of branching processes used to model biological populations, including those that exhibit logistic growth. In this paper we develop connections between the two, with the ultimate goal of determining when a population is more appropriately modelled with a PSDBP or a CBP. In particular, we state conditions for the existence of equivalent PSDBPs and CBPs, we then consider the subclass of CBPs with deterministic control functions (DCBPs), stating a necessary and sufficient condition for DCBP–PSDBP equivalence. Finally, we derive an upper bound on the total variation distance between non-equivalent DCBPs and PSDBPs with matching first and second moments and equal initial population size, and show that under certain conditions this bound tends to zero as the initial population size becomes large.

Suggested Citation

  • Braunsteins, Peter & Hautphenne, Sophie & Kerlidis, James, 2025. "Linking population-size-dependent and controlled branching processes," Stochastic Processes and their Applications, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:spapps:v:181:y:2025:i:c:s0304414924002643
    DOI: 10.1016/j.spa.2024.104556
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    References listed on IDEAS

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    1. González, M. & Molina, M. & del Puerto, I., 2004. "Limiting distribution for subcritical controlled branching processes with random control function," Statistics & Probability Letters, Elsevier, vol. 67(3), pages 277-284, April.
    2. Klebaner, Fima C., 1993. "Population-dependent branching processes with a threshold," Stochastic Processes and their Applications, Elsevier, vol. 46(1), pages 115-127, May.
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