Spine Decompositions and Limit Theorems for a Class of Critical Superprocesses

Yan Xia Ren, Renming Song, Zhenyao Sun

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we first establish a decomposition theorem for size-biased Poisson random measures. As consequences of this decomposition theorem, we get a spine decomposition theorem and a 2-spine decomposition theorem for some critical superprocesses. Then we use these spine decomposition theorems to give probabilistic proofs of the asymptotic behavior of the survival probability and Yaglom’s exponential limit law for critical superprocesses.

Original languageEnglish (US)
Pages (from-to)91-131
Number of pages41
JournalActa Applicandae Mathematicae
Volume165
Issue number1
DOIs
StatePublished - Feb 1 2020

Keywords

  • 2-Spine decomposition
  • Asymptotic behavior of the survival probability
  • Critical superprocess
  • Martingale change of measure
  • Size-biased Poisson random measure
  • Spine decomposition
  • Yaglom’s exponential limit law

ASJC Scopus subject areas

  • Applied Mathematics

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