| Issue |
ESAIM: PS
Volume 15, 2011
|
|
|---|---|---|
| Page(s) | 417 - 442 | |
| DOI | https://doi.org/10.1051/ps/2010011 | |
| Published online | 05 January 2012 | |
Continuous-time multitype branching processes conditioned on very late extinction*,**
Laboratoire d'Analyse et de Mathématiques Appliquées UMR 8050, Université Paris-Est Créteil, 61 avenue du Général de Gaulle, 94010 Créteil Cedex, France. sophie.penisson@u-pec.fr
Received:
19
October
2009
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.
Mathematics Subject Classification: 60J60 / 60J80
Key words: Multitype branching process / Feller diffusion process / conditioned branching process / diffusion limit / extinction / immortal particle / long-time behavior
© EDP Sciences, SMAI, 2011
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