L log L criterion for a class of superdiffusions

Rong Li Liu, Yan Xia Ren, Renming Song

Research output: Contribution to journalArticlepeer-review

Abstract

In Lyons, Pemantle and Peres (1995), a martingale change of measure method was developed in order to give an alternative proof of the Kesten-Stigum L log L theorem for single-type branching processes. Later, this method was extended to prove the L log L theorem for multiple-and general multiple-type branching processes in Biggins and Kyprianou (2004), Kurtz et al. (1997), and Lyons (1997). In this paper we extend this method to a class of superdiffusions and establish a Kesten-Stigum L log L type theorem for superdiffusions. One of our main tools is a spine decomposition of superdiffusions, which is a modification of the one in Englander and Kyprianou (2004).

Original languageEnglish (US)
Pages (from-to)479-496
Number of pages18
JournalJournal of Applied Probability
Volume46
Issue number2
DOIs
StatePublished - Jun 2009

Keywords

  • Diffusions
  • Kesten-stigum theorem
  • Martingale
  • Martingale change of measure
  • Poisson point process
  • Superdiffusions

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

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