Electronic Communications in Probability

Supercritical branching diffusions in random environment

Martin Hutzenthaler

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Abstract

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.

Article information

Source
Electron. Commun. Probab., Volume 16 (2011), paper no. 69, 781-791.

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465262025

Digital Object Identifier
doi:10.1214/ECP.v16-1685

Mathematical Reviews number (MathSciNet)
MR2868599

Zentralblatt MATH identifier
1243.60080

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60K37: Processes in random environments 60J60: Diffusion processes [See also 58J65]

Keywords
Branching diffusions in random environment BDRE supercriticality survival probability

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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


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