Limit theorems for conditioned multitype Dawson-Watanabe processes and Feller diffusions

  • A multitype Dawson-Watanabe process is conditioned, in subcritical and critical cases, on non-extinction in the remote future. On every finite time interval, its distribution is absolutely continuous with respect to the law of the unconditioned process. A martingale problem characterization is also given. Several results on the long time behavior of the conditioned mass process - the conditioned multitype Feller branching diffusion - are then proved. The general case is first considered, where the mutation matrix which models the interaction between the types, is irreducible. Several two-type models with decomposable mutation matrices are analyzed too .

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Author:Nicolas Champagnat, Sylvie Roelly
Series (Serial Number):Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (paper 065)
Document Type:Postprint
Year of Completion:2008
Publishing Institution:Universität Potsdam
Release Date:2008/05/23
Tag:conditioned; conditioned Feller diffusion; critical and subcritical Dawson-Watanabe process; multitype measure-valued branching processes
Source:Electronic journal of probability. - ISSN 1083-6489. - 13 (2008), paper no. 25, pp. 777 – 810
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Extern / Extern
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoKeine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht
Notes extern:AMS 2000 Subject Classification: 60J80 , 60G57
first published in:
Electronic journal of probability. - 13 (2008), paper no. 25, pp. 777 – 810
ISSN: 1083-6489 (Print)