Supercritical age-dependent branching processes with immigration
1974 ◽
Vol 11
(04)
◽
pp. 695-702
◽
Keyword(s):
A branching process with immigration of the following type is considered. For everyi, a random numberNiof particles join the system at time. These particles evolve according to a one-dimensional age-dependent branching process with offspring p.g.f.and life time distributionG(t). Assume. Then it is shown thatZ(t)e–αtconverges in distribution to an extended real-valued random variableYwhereais the Malthusian parameter. We do not require the sequences {τi} or {Ni} to be independent or identically distributed or even mutually independent.