Electronic Journal of Probability
- Electron. J. Probab.
- Volume 13 (2008), paper no. 25, 777-810.
Limit theorems for conditioned multitype Dawson-Watanabe processes and Feller diffusions
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.
Electron. J. Probab., Volume 13 (2008), paper no. 25, 777-810.
Accepted: 6 May 2008
First available in Project Euclid: 1 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60G57: Random measures
This work is licensed under aCreative Commons Attribution 3.0 License.
Champagnat, Nicolas; Roelly, Sylvie. Limit theorems for conditioned multitype Dawson-Watanabe processes and Feller diffusions. Electron. J. Probab. 13 (2008), paper no. 25, 777--810. doi:10.1214/EJP.v13-504. https://projecteuclid.org/euclid.ejp/1464819098