## Electronic Journal of Probability

### A Williams decomposition for spatially dependent superprocesses

#### Abstract

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.

#### Article information

Source
Electron. J. Probab., Volume 18 (2013), paper no. 37, 43 pp.

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

https://projecteuclid.org/euclid.ejp/1465064262

Digital Object Identifier
doi:10.1214/EJP.v18-1801

Mathematical Reviews number (MathSciNet)
MR3035765

Zentralblatt MATH identifier
1294.60104

Rights

#### Citation

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

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