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Limiting behaviour of two-level measure-branching

Part of: Markov processes Limit theorems Stochastic analysis

Published online by Cambridge University Press:  01 July 2016

Alison M. Etheridge
Alison M. Etheridge*
Affiliation:
University of Edinburgh
*
* Postal address: Department of Mathematics and Statistics, University of Edinburgh, King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, UK.
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Abstract

A measure-valued diffusion approximation to a two-level branching structure was introduced in Dawson and Hochberg (1991) where it was shown that conditioned on non-extinction at time t, and appropriately rescaled, the process converges as t → ∞to a non-trivial limiting distribution. Here we discuss a different approach to conditioning on non-extinction (popular in one-level branching) and relate the two limiting distributions.

Keywords

MULTILEVEL BRANCHINGMEASURE-VALUED PROCESSCONDITIONAL LIMIT THEOREM

MSC classification

Primary: 60J57: Multiplicative functionals
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60F05: Central limit and other weak theorems 60H15: Stochastic partial differential equations
Type
Research Article
Information
Advances in Applied Probability , Volume 25 , Issue 4 , December 1993 , pp. 773 - 782
Copyright
Copyright © Applied Probability Trust 1993 

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Footnotes

Research carried out while the author was Neyman Assistant Professor at the University of California, Berkeley.

References

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