Electronic Journal of Probability
- Electron. J. Probab.
- Volume 18 (2013), paper no. 37, 43 pp.
A Williams decomposition for spatially dependent superprocesses
We present a genealogy for superprocesses with a non-homogeneous quadratic branching mechanism, relying on a weighted version of the superprocess introduced by Engländer and Pinsky and a Girsanov theorem. We then decompose this genealogy with respect to the last individual alive (Williams' decomposition). Letting the extinction time tend to infinity, we get the Q-process by looking at the superprocess from the root, and define another process by looking from the top. Examples including the multitype Feller diffusion (investigated by Champagnat and Roelly) and the superdiffusion are provided.
Electron. J. Probab., Volume 18 (2013), paper no. 37, 43 pp.
Accepted: 12 March 2013
First available in Project Euclid: 4 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 60J55: Local time and additive functionals 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
This work is licensed under a Creative Commons Attribution 3.0 License.
Delmas, Jean-François; Hénard, Olivier. A Williams decomposition for spatially dependent superprocesses. Electron. J. Probab. 18 (2013), paper no. 37, 43 pp. doi:10.1214/EJP.v18-1801. https://projecteuclid.org/euclid.ejp/1465064262