Immortal particle for a catalytic branching process

Ilie Grigorescu, Min Kang

Research output: Contribution to journalArticle

13 Scopus citations

Abstract

We study the existence and asymptotic properties of a conservative branching particle system driven by a diffusion with smooth coefficients for which birth and death are triggered by contact with a set. Sufficient conditions for the process to be non-explosive are given. In the Brownian motions case the domain of evolution can be non-smooth, including Lipschitz, with integrable Martin kernel. The results are valid for an arbitrary number of particles and non-uniform redistribution after branching. Additionally, with probability one, it is shown that only one ancestry line survives. In special cases, the evolution of the surviving particle is studied and for a two particle system on a half line we derive explicitly the transition function of a chain representing the position at successive branching times.

Original languageEnglish (US)
Pages (from-to)333-361
Number of pages29
JournalProbability Theory and Related Fields
Volume153
Issue number1-2
DOIs
StatePublished - Jun 1 2012

Keywords

  • Doeblin condition
  • Fleming-Viot branching
  • Immortal particle
  • Jump diffusion process
  • Martin kernel

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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