We decompose the genealogy of a general superprocess with spatially dependent branching mechanism with respect to the last individual alive (Williams decomposition). This is a generalization of the main result of Delmas and Hénard  where only superprocesses with spatially dependent quadratic branching mechanism were considered. As an application of the Williams decomposition, we prove that, for some superprocesses, the normalized total measure will converge to a point measure at its extinction time. This partially generalizes a result of Tribe  in the sense that our branching mechanism is more general.
- Spatially dependent branching mechanism
- Williams decomposition
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty