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Almost sure convergence of measure-valued branching processes: a critical exponent

Published online by Cambridge University Press:  14 November 2011

Alison M. Etheridge
Alison M. Etheridge
Affiliation:
Department of Mathematics and Statistics, University of Edinburgh, Edinburgh, U.K.
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Abstract

A large class of measure-valued critical branching processes can be classified in terms of a parameter ρ which arises as a measure of the recurrence of the underlying spatial Markov process. By establishing upper and lower bounds for the total weighted occupation time process, it is shown that if a measure-valued process is started from an invariant measure of its underlying spatial process, then a necessary and sufficient condition for (a.s.) local extinction is that ρ > 0.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 4 , 1994 , pp. 811 - 823
Copyright
Copyright © Royal Society of Edinburgh 1994

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