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August 1997 On the convergence of multitype branching processes with varying environments
Owen Dafydd Jones
Ann. Appl. Probab. 7(3): 772-801 (August 1997). DOI: 10.1214/aoap/1034801253

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.

Citation

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Owen Dafydd Jones. "On the convergence of multitype branching processes with varying environments." Ann. Appl. Probab. 7 (3) 772 - 801, August 1997. https://doi.org/10.1214/aoap/1034801253

Information

Published: August 1997
First available in Project Euclid: 16 October 2002

zbMATH: 0885.60077
MathSciNet: MR1459270
Digital Object Identifier: 10.1214/aoap/1034801253

Subjects:
Primary: 60J80
Secondary: 15A48

Keywords: branching process , ergodic matrix products , multitype , varying environment

Rights: Copyright © 1997 Institute of Mathematical Statistics

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Vol.7 • No. 3 • August 1997
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