Multitype branching processes and Feller diffusion processes are conditioned on very late extinction. The conditioned laws are expressed as Doob h-transforms of the unconditioned laws, and an interpretation of the conditioned paths for the branching process is given, via the immortal particle. We study different limits for the conditioned process (increasing delay of extinction, long-time behavior, scaling limit) and provide an exhaustive list of exchangeability results.
Mots clés : multitype branching process, Feller diffusion process, conditioned branching process, diffusion limit, extinction, immortal particle, long-time behavior
@article{PS_2011__15__417_0,
author = {P\'enisson, Sophie},
title = {Continuous-time multitype branching processes conditioned on very late extinction},
journal = {ESAIM: Probability and Statistics},
pages = {417--442},
publisher = {EDP-Sciences},
volume = {15},
year = {2011},
doi = {10.1051/ps/2010011},
mrnumber = {2870524},
zbl = {1278.60134},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps/2010011/}
}
TY - JOUR AU - Pénisson, Sophie TI - Continuous-time multitype branching processes conditioned on very late extinction JO - ESAIM: Probability and Statistics PY - 2011 SP - 417 EP - 442 VL - 15 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2010011/ DO - 10.1051/ps/2010011 LA - en ID - PS_2011__15__417_0 ER -
%0 Journal Article %A Pénisson, Sophie %T Continuous-time multitype branching processes conditioned on very late extinction %J ESAIM: Probability and Statistics %D 2011 %P 417-442 %V 15 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps/2010011/ %R 10.1051/ps/2010011 %G en %F PS_2011__15__417_0
Pénisson, Sophie. Continuous-time multitype branching processes conditioned on very late extinction. ESAIM: Probability and Statistics, Tome 15 (2011), pp. 417-442. doi : 10.1051/ps/2010011. http://www.numdam.org/articles/10.1051/ps/2010011/
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