Lifetime and compactness of range for super-Brownian motion with a general branching mechanism

Yuan-Chung Sheu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

Let X be a super-Brownian motion with a general (time-space) homogeneous branching mechanism. We study a relation between lifetime and compactness of range for X. Under a restricted condition on the branching mechanism, we show that the set X survives is the same as that the range of X is unbounded. (For α-branching super-Brownian motion, 1 < α ≤ 2, similar results were obtained earlier by Iscoe (1988) and Dynkin (1991). ) We also give an interesting example in that case X dies out in finite time, but it has an unbounded range.

Original languageEnglish
Pages (from-to)129-141
Number of pages13
JournalStochastic Processes and their Applications
Volume70
Issue number1
DOIs
StatePublished - 1 Oct 1997

Keywords

  • Branching mechanism
  • Compactness of range
  • Lifetime
  • Super-Brownian motion
  • Support

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