Williams decomposition for superprocesses

Yan Xia Ren, Renming Song, Rui Zhang

Research output: Contribution to journalArticlepeer-review


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 [5] 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 [27] in the sense that our branching mechanism is more general.

Original languageEnglish (US)
Article number23
JournalElectronic Journal of Probability
StatePublished - Jan 1 2018


  • Genealogy
  • Spatially dependent branching mechanism
  • Superprocesses
  • Williams decomposition

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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