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2011 Supercritical branching diffusions in random environment
Martin Hutzenthaler
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Electron. Commun. Probab. 16: 781-791 (2011). DOI: 10.1214/ECP.v16-1685


Supercritical branching processes in constant environment conditioned on eventual extinction are known to be subcritical branching processes. The case of random environment is more subtle. A supercritical branching diffusion in random environment (BDRE) conditioned on eventual extinction of the population is not a branching diffusion in a homogeneous environment. However the law of the population size of a supercritical BDRE (averaged over the environment) conditioned on eventual extinction is equal to the law of the population size of a subcritical BDRE (averaged over the environment). As a consequence, supercritical BDREs have a phase transition which is similar to a well-known phase transition of subcritical branching processes in random environment.


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Martin Hutzenthaler. "Supercritical branching diffusions in random environment." Electron. Commun. Probab. 16 781 - 791, 2011.


Accepted: 6 December 2011; Published: 2011
First available in Project Euclid: 7 June 2016

zbMATH: 1243.60080
MathSciNet: MR2868599
Digital Object Identifier: 10.1214/ECP.v16-1685

Primary: 60J80
Secondary: 60J60, 60K37


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