Extinction of branching symmetric α-stable processes

Yuichi Shiozawa

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We give a criterion for extinction or local extinction of branching symmetric α-stable processes in terms of the principal eigenvalue for time-changed processes of symmetric α-stable processes. Here the branching rate and the branching mechanism are spatially dependent. In particular, the branching rate is allowed to be singular with respect to the Lebesgue measure. We apply this criterion to some branching processes.

Original languageEnglish
Pages (from-to)1077-1090
Number of pages14
JournalJournal of Applied Probability
Volume43
Issue number4
DOIs
Publication statusPublished - Dec 1 2006

Keywords

  • Branching process
  • Brownian motion
  • Extinction
  • Gaugeability
  • Local extinction
  • Principal eigenvalue
  • Symmetric α-stable process
  • Time change

ASJC Scopus subject areas

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

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