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Approximate modeling for supercritical Galton-Watson branching processes with compound Poisson-gamma distribution

Kyoya Uemura*, Tomoyuki Obuchi, and Toshiyuki Tanaka

  • *Contact author: uemura.kyoya.n08@kyoto-u.jp
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Phys. Rev. Research 8, 013230 – Published 2 March, 2026

DOI: https://doi.org/10.1103/w3yn-jpt5

Abstract

We study asymptotic properties of supercritical Galton-Watson (GW) branching processes in the asymptotic where the mean of the offspring distribution approaches 1 from above. We show that the population-size distribution of the GW branching processes at a sufficiently large generation in this asymptotic can be approximated by a compound Poisson-gamma distribution. Numerical experiments revealed that the compound Poisson-gamma models were in good agreement with the corresponding GW models for sufficiently large generations under a reasonable parameter regime. Our results can be regarded as supporting the use of the compound Poisson-gamma model as a model for cascaded multiplication processes.

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References (43)

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Phys. Rev. Research 8, 013230– Published 2 March, 2026
  • Received 26 October 2025
  • Accepted 13 January 2026
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