Spine decomposition and L log L criterion for superprocesses with non-local branching mechanisms

Yan Xia Ren, Renming Song, Ting Yang

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we provide a pathwise spine decomposition for superprocesses with both local and non-local branching mechanisms under a martingale change of measure. This result complements earlier results established for superprocesses with purely local branching mechanisms and for multitype superprocesses. As an application of this decomposition, we obtain necessary/sufficient conditions for the limit of the fundamental martingale to be non-degenerate. In particular, we obtain extinction properties of superprocesses with non-local branching mechanisms as well as a Kesten-Stigum Llog L theorem for the fundamental martingale.

Original languageEnglish (US)
Pages (from-to)163-208
Number of pages46
JournalAlea
Volume19
Issue number1
DOIs
StatePublished - 2022

Keywords

  • Local branching mechanism
  • Martingale
  • Non-local branching mechanism
  • Spine decomposition
  • Superprocess
  • Weak local extinction

ASJC Scopus subject areas

  • Statistics and Probability

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