@article{ECP1685,
author = {Martin Hutzenthaler},
title = {Supercritical branching diffusions in random environment},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {16},
year = {2011},
keywords = {Branching diffusions in random environment, BDRE, supercriticality, survival probability},
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.},
pages = {no. 69, 781-791},
issn = {1083-589X},
doi = {10.1214/ECP.v16-1685},
url = {http://ecp.ejpecp.org/article/view/1685}}