Supercritical branching diffusions in random environment

Details Supercritical branching diffusions in random environment Supercritical branching diffusions in random environment

2011-09-08

arxiv.org/abs/1109.1849v1

Mathematics

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12 pages

Scientific paper

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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