Supercritical branching diffusions in random environment
Probability
2013-10-02 v2
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 BDRE. However the quenched law of the population size of a supercritical BDRE conditioned on eventual extinction is equal to the quenched law of the population size of a subcritical BDRE. 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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Cite
@article{arxiv.1109.1849,
title = {Supercritical branching diffusions in random environment},
author = {Martin Hutzenthaler},
journal= {arXiv preprint arXiv:1109.1849},
year = {2013}
}
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11 pages