Continuous-time multitype branching processes conditioned on very late extinction***

Sophie Pénisson

ESAIM: Probability and Statistics (2012)

  • Volume: 15, page 417-442
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Pénisson, Sophie. "Continuous-time multitype branching processes conditioned on very late extinction***." ESAIM: Probability and Statistics 15 (2012): 417-442. <http://eudml.org/doc/222470>.

@article{Pénisson2012,
abstract = { 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. },
author = {Pénisson, Sophie},
journal = {ESAIM: Probability and Statistics},
keywords = {Multitype branching process; Feller diffusion process; conditioned branching process; diffusion limit; extinction; immortal particle; long-time behavior; multitype branching process; Feller diffusion},
language = {eng},
month = {1},
pages = {417-442},
publisher = {EDP Sciences},
title = {Continuous-time multitype branching processes conditioned on very late extinction***},
url = {http://eudml.org/doc/222470},
volume = {15},
year = {2012},
}

TY - JOUR
AU - Pénisson, Sophie
TI - Continuous-time multitype branching processes conditioned on very late extinction***
JO - ESAIM: Probability and Statistics
DA - 2012/1//
PB - EDP Sciences
VL - 15
SP - 417
EP - 442
AB - 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.
LA - eng
KW - Multitype branching process; Feller diffusion process; conditioned branching process; diffusion limit; extinction; immortal particle; long-time behavior; multitype branching process; Feller diffusion
UR - http://eudml.org/doc/222470
ER -

References

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