Abstract
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.
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