Abstract
A general multitype branching process in which individuals are counted according to some possibly type-dependent characteristic may be defined along the lines laid out by Jagers (1969, 1974) for the single type process. In the critical case, the probability of nonextinction at time $t$ is shown to be $O(t^{-1})$, and, conditioned on nonextinction at time $t$, the totals of the characteristic counts, normalized by $t$, are shown to satisfy an exponential limit law, under weak (essentially, second moment) hypotheses.
Citation
John M. Holte. "Critical Multitype Branching Processes." Ann. Probab. 10 (2) 482 - 495, May, 1982. https://doi.org/10.1214/aop/1176993871
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