## The Annals of Applied Probability

### On the convergence of multitype branching processes with varying environments

Owen Dafydd Jones

#### Abstract

Using the ergodic theory of nonnegative matrices, conditions are obtained for the $L^2$ and almost sure convergence of a supercritical multitype branching process with varying environment, normed by its mean. We also give conditions for the extinction probability of the limit to equal that of the process.

The theory developed allows for different types to grow at different rates, and an example of this is given, taken from the construction of a spatially inhomogeneous diffusion on the Sierpinski gasket.

#### Article information

Source
Ann. Appl. Probab., Volume 7, Number 3 (1997), 772-801.

Dates
First available in Project Euclid: 16 October 2002

https://projecteuclid.org/euclid.aoap/1034801253

Digital Object Identifier
doi:10.1214/aoap/1034801253

Mathematical Reviews number (MathSciNet)
MR1459270

Zentralblatt MATH identifier
0885.60077

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 15A48

#### Citation

Jones, Owen Dafydd. On the convergence of multitype branching processes with varying environments. Ann. Appl. Probab. 7 (1997), no. 3, 772--801. doi:10.1214/aoap/1034801253. https://projecteuclid.org/euclid.aoap/1034801253

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