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May, 1982 Critical Multitype Branching Processes
John M. Holte
Ann. Probab. 10(2): 482-495 (May, 1982). DOI: 10.1214/aop/1176993871

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.

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John M. Holte. "Critical Multitype Branching Processes." Ann. Probab. 10 (2) 482 - 495, May, 1982. https://doi.org/10.1214/aop/1176993871

Information

Published: May, 1982
First available in Project Euclid: 19 April 2007

zbMATH: 0481.60076
MathSciNet: MR665602
Digital Object Identifier: 10.1214/aop/1176993871

Subjects:
Primary: 60F05
Secondary: 60J80

Keywords: asymptotic nonextinction probability , Critical branching process , exponential limit law , multitype branching process , renewal theory

Rights: Copyright © 1982 Institute of Mathematical Statistics

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Vol.10 • No. 2 • May, 1982
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