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2008 Limit theorems for conditioned multitype Dawson-Watanabe processes and Feller diffusions
Nicolas Champagnat, Sylvie Roelly
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Electron. J. Probab. 13: 777-810 (2008). DOI: 10.1214/EJP.v13-504


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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Nicolas Champagnat. Sylvie Roelly. "Limit theorems for conditioned multitype Dawson-Watanabe processes and Feller diffusions." Electron. J. Probab. 13 777 - 810, 2008.


Accepted: 6 May 2008; Published: 2008
First available in Project Euclid: 1 June 2016

zbMATH: 1189.60154
MathSciNet: MR2399296
Digital Object Identifier: 10.1214/EJP.v13-504

Primary: 60J80
Secondary: 60G57

Keywords: conditioned Feller diffusion , conditionedDawson-Watanabe process , critical and subcritical Dawson-Watanabeprocess , long time behavior , multitype measure-valued branching processes , remote survival


Vol.13 • 2008
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