Critical Galton–Watson Processes with Overlapping Generations
Keyword(s):
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 .
1987 ◽
Vol 24
(03)
◽
pp. 768-772
◽
Keyword(s):
1985 ◽
Vol 22
(01)
◽
pp. 223-227
◽
Keyword(s):
2011 ◽
Vol 48
(02)
◽
pp. 576-582
◽
2019 ◽
Vol 56
(4)
◽
pp. 1122-1150
◽
2011 ◽
Vol 48
(2)
◽
pp. 576-582
◽
2013 ◽
Vol 50
(03)
◽
pp. 791-800
◽