Critical Galton-Watson processes with overlapping generations

2021/07/23 by Sagitov, Serik
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2107.11031

Abstract

A properly scaled critical Galton-Watson process converges to a continuous state critical branching process ξ(⋅) as the number of initial individuals tends to infinity. We extend this classical result by allowing for overlapping generations and considering a wide class of population counts. The main result of the paper establishes a convergence of the finite dimensional distributions for a scaled vector of multiple population counts. The set of the limiting distributions is conveniently represented in terms of integrals (∫₀^yξ(y-u)du^γ, y≥0) with a pertinent γ≥0.

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