The Annals of Probability

On the Growth of the Multitype Supercritical Branching Process in a Random Environment

Harry Cohn

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Abstract

Let $\{\mathbf{Z}_n\}$ be a multitype branching process in a random environment (MBPRE) which grows to infinity with positive probability for almost all environmental sequences. Under some conditions involving the first two moments of the environmental sequence, it is shown that dividing the $\{\mathbf{Z}_n\}$ components by their environment-conditioned expectations yields a sequence convergent in $L^2$ to a random vector with equal components.

Article information

Source
Ann. Probab., Volume 17, Number 3 (1989), 1118-1123.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991259

Digital Object Identifier
doi:10.1214/aop/1176991259

Mathematical Reviews number (MathSciNet)
MR1009447

Zentralblatt MATH identifier
0693.60072

JSTOR
links.jstor.org

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60F25: $L^p$-limit theorems

Keywords
Branching random environment multitype Furstenberg-Kesten theorem martingale $L^2$-convergence

Citation

Cohn, Harry. On the Growth of the Multitype Supercritical Branching Process in a Random Environment. Ann. Probab. 17 (1989), no. 3, 1118--1123. doi:10.1214/aop/1176991259. https://projecteuclid.org/euclid.aop/1176991259


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