Work

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

Year: 2026

Type: article

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.

Source: Physical Review Research

DOI: 10.1103/w3yn-jpt5

Authors: Kyoya Uemura, Tomoyuki Obuchi, Toshiyuki Tanaka

Institution: Kyoto University

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,625

Funders: Japan Society for the Promotion of Science, Japan Science and Technology Agency, Core Research for Evolutional Science and Technology