Affiliation:
1. Department of Mathematical Sciences , Chalmers University of Technology and University of Gothenburg , Goteborg , Sweden
Abstract
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
.
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Statistics, Probability and Uncertainty,Safety, Risk, Reliability and Quality,Statistics and Probability
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Limit laws for decomposable critical branching processes,
Z. Wahrsch. Verw. Gebiete 46 (1978/79), no. 1, 13–43.
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