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.
Citation
Nicolas Champagnat. Sylvie Roelly. "Limit theorems for conditioned multitype Dawson-Watanabe processes and Feller diffusions." Electron. J. Probab. 13 777 - 810, 2008. https://doi.org/10.1214/EJP.v13-504
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