## The Annals of Probability

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

Harry Cohn

#### 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

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
Secondary: 60F25: $L^p$-limit theorems