Critical Galton-Watson Processes with Overlapping Generations

A properly scaled critical Galton-Watson process converges to a continuous state critical branching process ζ(\ub7) 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