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

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

2007-07-24

arxiv.org/abs/0707.3504v2

Electronic Journal of Probability 13, 25 (2008) 777-810

Mathematics

Probability

Scientific paper

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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