Open Access
October, 1989 Geometric Growth in Near-Supercritical Population Size Dependent Multitype Galton-Watson Processes
Fima C. Klebaner
Ann. Probab. 17(4): 1466-1477 (October, 1989). DOI: 10.1214/aop/1176991167


We consider a multitype population size dependent branching process in discrete time. A process is considered to be near-supercritical if the mean matrices of offspring distributions approach the mean matrix of a supercritical process as the population size increases. We show that if the convergence of the means to the supercritical mean is fast enough and the second moments of offspring distributions do not grow too fast as the population size increases, then the process grows geometrically fast. Similarly to the classical multitype Galton-Watson process, the process grows at the geometric rate determined by the largest eigenvalue of the limiting matrix in the direction of the corresponding left eigenvector.


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Fima C. Klebaner. "Geometric Growth in Near-Supercritical Population Size Dependent Multitype Galton-Watson Processes." Ann. Probab. 17 (4) 1466 - 1477, October, 1989.


Published: October, 1989
First available in Project Euclid: 19 April 2007

zbMATH: 0694.60079
MathSciNet: MR1048939
Digital Object Identifier: 10.1214/aop/1176991167

Primary: 60J80
Secondary: 60J05

Keywords: growth rates , multidimensional Markov chains , Multitype branching processes

Rights: Copyright © 1989 Institute of Mathematical Statistics

Vol.17 • No. 4 • October, 1989
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