Critical Galton-Watson Processes with Overlapping Generations
Artikel i vetenskaplig tidskrift, 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

Författare

Serik Sagitov

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Göteborgs universitet

Stochastics and Quality Control

23672390 (ISSN) 23672404 (eISSN)

Vol. 36 2 87-110

Ämneskategorier

Beräkningsmatematik

Sannolikhetsteori och statistik

Matematisk analys

DOI

10.1515/eqc-2021-0027

Mer information

Senast uppdaterat

2022-04-05