## The Annals of Probability

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

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

#### 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