Limit theorems for conditioned multitype Dawson-Watanabe processes and Feller diffusions
Probability
2011-12-05 v2
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.
Cite
@article{arxiv.0707.3504,
title = {Limit theorems for conditioned multitype Dawson-Watanabe processes and Feller diffusions},
author = {Nicolas Champagnat and Sylvie Roelly},
journal= {arXiv preprint arXiv:0707.3504},
year = {2011}
}