Open Access
2013 A Williams decomposition for spatially dependent superprocesses
Jean-François Delmas, Olivier Hénard
Author Affiliations +
Electron. J. Probab. 18: 1-43 (2013). DOI: 10.1214/EJP.v18-1801


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.


Download Citation

Jean-François Delmas. Olivier Hénard. "A Williams decomposition for spatially dependent superprocesses." Electron. J. Probab. 18 1 - 43, 2013.


Accepted: 12 March 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1294.60104
MathSciNet: MR3035765
Digital Object Identifier: 10.1214/EJP.v18-1801

Primary: 60J25
Secondary: 60J55 , 60J80

Keywords: genealogy , H-transform , Q-process , Spatially dependent superprocess , Williams' decomposition

Vol.18 • 2013
Back to Top