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February 1996 Branching processes with local dependencies
Peter Olofsson
Ann. Appl. Probab. 6(1): 238-268 (February 1996). DOI: 10.1214/aoap/1034968073


A general multitype branching process with sibling dependencies is considered. The dependencies within a group of siblings are described by a joint probability measure, determined by the structure of that particular group. The process is analyzed by means of the embedded macro process, consisting of sibling groups. It is shown that the regular asymptotic behavior of the sibling-dependent process is guaranteed by conditions on the individual reproductions, and that these conditions are exactly the same as those normally required for an ordinary independent process that has the same individual marginals. Convergence results for the expected population size as well as the actual population size are given, and the stable population is described. The sibling-dependent process and the ordinary independent process with the same marginals are compared; some simple examples illustrate the differences and similarities. The results are extended to more general dependencies that are local in the family tree.


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Peter Olofsson. "Branching processes with local dependencies." Ann. Appl. Probab. 6 (1) 238 - 268, February 1996.


Published: February 1996
First available in Project Euclid: 18 October 2002

zbMATH: 0863.60080
MathSciNet: MR1389839
Digital Object Identifier: 10.1214/aoap/1034968073

Primary: 60J80
Secondary: 60F25

Keywords: general branching process , local dependencies , macro process , multitype , sibling dependencies , stable population

Rights: Copyright © 1996 Institute of Mathematical Statistics


Vol.6 • No. 1 • February 1996
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