Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 16 (2011), paper no. 69, 781-791.
Supercritical branching diffusions in random environment
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.
Electron. Commun. Probab., Volume 16 (2011), paper no. 69, 781-791.
Accepted: 6 December 2011
First available in Project Euclid: 7 June 2016
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Hutzenthaler, Martin. Supercritical branching diffusions in random environment. Electron. Commun. Probab. 16 (2011), paper no. 69, 781--791. doi:10.1214/ECP.v16-1685. https://projecteuclid.org/euclid.ecp/1465262025