## Electronic Journal of Probability

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

#### 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.

#### Article information

Source
Electron. J. Probab., Volume 13 (2008), paper no. 25, 777-810.

Dates
Accepted: 6 May 2008
First available in Project Euclid: 1 June 2016

https://projecteuclid.org/euclid.ejp/1464819098

Digital Object Identifier
doi:10.1214/EJP.v13-504

Mathematical Reviews number (MathSciNet)
MR2399296

Zentralblatt MATH identifier
1189.60154

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60G57: Random measures

Rights

#### Citation

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

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