Critical Galton-Watson Processes with Overlapping Generations
Journal article, 2021

A properly scaled critical Galton-Watson process converges to a continuous state critical branching process ζ(·) 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 (∫0yζ(y-u)duγ,γ≥0) with a pertinent γ≥0.

Continuous State Branching Process

Finite-Dimensional Distributions

Decomposable Critical Galton-Watson Process

Critical Branching Process


Serik Sagitov

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

University of Gothenburg

Stochastics and Quality Control

23672390 (ISSN) 23672404 (eISSN)

Vol. 36 2 87-110

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Mathematical Analysis



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4/5/2022 5