On the convergence of multi-type branching processes with varying environments

Owen Dafydd Jones

Abstract: Using the ergodic theory of non-negative 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.

Acknowledgement: This worked was funded by the Australian Research Council.

The author:

• Owen Jones, Discipline of Mathematics, The University of Queensland. Owen.Jones@maths.anu.edu.au

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Last modified: 6th July 1998