Critical Galton–Watson Processes with Overlapping Generations

Sagitov Serik ()
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Sagitov Serik: Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Goteborg, Sweden

Stochastics and Quality Control, 2021, vol. 36, issue 2, 87-110

Abstract: A properly scaled critical Galton–Watson process converges to a continuous state critical branching process ξ ⁢ ( ⋅ ) \xi(\,{\cdot}\,) 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 y ξ ⁢ ( y - u ) ⁢ d u γ \int_{0}^{y}\xi(y-u)\,du^{\gamma} , y ≥ 0 y\geq 0 ) with a pertinent γ ≥ 0 \gamma\geq 0 .

Keywords: Critical Branching Process; Continuous State Branching Process; Finite-Dimensional Distributions; Decomposable Critical Galton–Watson Process (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1515/eqc-2021-0027

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