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.
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