A Williams decomposition for spatially dependent superprocesses

Jean-François Delmas (1) , Olivier Hénard (1)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique

We present a genealogy for superprocesses with a non-homogeneous quadratic branching mechanism, relying on a weighted version of the superprocess and a Girsanov theorem. We then decompose this genealogy with respect to the last individual alive (William's 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 diff usion and the superdiffusion are provided.

Mots clés: Spatially dependent superprocess; Williams' decomposition; genealogy; h-transform; Q-process

Domaines: Probabilités [math.PR]

Jean-François Delmas, Olivier Hénard. A Williams decomposition for spatially dependent superprocesses. Electronic Journal of Probability, 2013, 18, pp.1-43. ⟨10.1214/EJP.v18-1801⟩. ⟨hal-00601539⟩