The Annals of Probability

Supercritical Multitype Branching Processes

Fred M. Hoppe

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Abstract

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.

Article information

Source
Ann. Probab., Volume 4, Number 3 (1976), 393-401.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996088

Digital Object Identifier
doi:10.1214/aop/1176996088

Mathematical Reviews number (MathSciNet)
MR420892

Zentralblatt MATH identifier
0361.60063

JSTOR
links.jstor.org

Subjects
Primary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40]
Secondary: 60F15: Strong theorems

Keywords
Multitype Galton-Watson process supercritical positively regular normalizing constants Poincare functional equation regular variation

Citation

Hoppe, Fred M. Supercritical Multitype Branching Processes. Ann. Probab. 4 (1976), no. 3, 393--401. doi:10.1214/aop/1176996088. https://projecteuclid.org/euclid.aop/1176996088


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