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

Author

Serik Sagitov

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

University of Gothenburg

Stochastics and Quality Control

23672390 (ISSN) 23672404 (eISSN)

Vol. In Press

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Mathematical Analysis

DOI

10.1515/eqc-2021-0027

More information

Latest update

11/29/2021