Open Access
June, 1976 Supercritical Multitype Branching Processes
Fred M. Hoppe
Ann. Probab. 4(3): 393-401 (June, 1976). DOI: 10.1214/aop/1176996088


We show that there always exists a sequence of normalizing constants for the supercritical multitype Galton-Watson process so that the normalized sequence converges in probability to a limit which is proper and not identically zero. The Laplace-Stieltjes transform of the limit random variable is characterized as the unique solution under certain conditions of a vector Poincare functional equation.


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Fred M. Hoppe. "Supercritical Multitype Branching Processes." Ann. Probab. 4 (3) 393 - 401, June, 1976.


Published: June, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0361.60063
MathSciNet: MR420892
Digital Object Identifier: 10.1214/aop/1176996088

Primary: 60J20
Secondary: 60F15

Keywords: Multitype Galton-Watson process , Normalizing constants , Poincare functional equation , positively regular , regular variation , supercritical

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 3 • June, 1976
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