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

Published online by Cambridge University Press:  05 January 2012

Sophie Pénisson
Sophie Pénisson*
Affiliation:
Laboratoire d'Analyse et de Mathématiques Appliquées UMR 8050, Université Paris-Est Créteil, 61 avenue du Général de Gaulle, 94010 Créteil Cedex, France. [email protected]
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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.

Keywords

Multitype branching processFeller diffusion processconditioned branching processdiffusion limitextinctionimmortal particlelong-time behavior
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 15: Supplement: In honor of Marc Yor , 2011 , pp. 417 - 442
Copyright
© EDP Sciences, SMAI, 2011

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