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 Electronic Journal of Probability > Vol. 13 (2008) > Paper 25 open journal systems 


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

Nicolas Champagnat, INRIA, France
Sylvie Roelly, Potsdam University, Germany


Abstract
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.


Full text: PDF

Pages: 777-810

Published on: May 6, 2008
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Electronic Journal of Probability. ISSN: 1083-6489