Branching processes in Lévy processes: Laplace functionals of snakes and superprocesses

Jean François Le Gall, Yves Le Jan

Research output: Contribution to journalArticlepeer-review

Abstract

We use the exploration process introduced in a previous work to develop a new construction of superprocesses with a general branching mechanism. This construction depends on a path-valued process called the Lévy snake, which is of independent interest. Our method of proof involves a calculation of the Laplace functional of the occupation field of the Lévy snake. This calculation relies on an evaluation of the corresponding moment functionals, which requires precise information about the underlying genealogical structure.

Original languageEnglish (US)
Pages (from-to)1407-1432
Number of pages26
JournalAnnals of Probability
Volume26
Issue number4
StatePublished - Oct 1998

Keywords

  • Branching process
  • Exploration process
  • Laplace functionals
  • Lévy process
  • Lévy snake
  • Moment functionals
  • Superprocess

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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