Supercritical multitype branching processes: the ancestral types of typical individuals

Georgii H-O, Baake E (2003)
Adv. Appl. Prob. 35 (2003), 1090-1110.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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For supercritical multitype branching processes in continuous time, weinvestigate the evolution of types along those lineages that survive up to sometime t. We establish almost-sure convergence theorems for both time andpopulation averages of ancestral types (conditioned on non-extinction), andidentify the mutation process describing the type evolution along typicallineages. An important tool is a representation of the family tree in terms ofa suitable size-biased tree with trunk. As a by-product, this representationallows a `conceptual proof' (in the sense of Kurtz, Lyons, Pemantle, Peres1997) of the continuous-time version of the Kesten-Stigum theorem.
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Adv. Appl. Prob. 35 (2003), 1090-1110
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Georgii H-O, Baake E. Supercritical multitype branching processes: the ancestral types of typical individuals. Adv. Appl. Prob. 35 (2003), 1090-1110. 2003.
Georgii, H. - O., & Baake, E. (2003). Supercritical multitype branching processes: the ancestral types of typical individuals. Adv. Appl. Prob. 35 (2003), 1090-1110
Georgii, H. - O., and Baake, E. (2003). Supercritical multitype branching processes: the ancestral types of typical individuals. Adv. Appl. Prob. 35 (2003), 1090-1110.
Georgii, H.-O., & Baake, E., 2003. Supercritical multitype branching processes: the ancestral types of typical individuals. Adv. Appl. Prob. 35 (2003), 1090-1110.
H.-O. Georgii and E. Baake, “Supercritical multitype branching processes: the ancestral types of typical individuals”, Adv. Appl. Prob. 35 (2003), 1090-1110, 2003.
Georgii, H.-O., Baake, E.: Supercritical multitype branching processes: the ancestral types of typical individuals. Adv. Appl. Prob. 35 (2003), 1090-1110. (2003).
Georgii, Hans-Otto, and Baake, Ellen. “Supercritical multitype branching processes: the ancestral types of typical individuals”. Adv. Appl. Prob. 35 (2003), 1090-1110 (2003).

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arXiv: math/0302049

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