Limit theorems for a class of critical superprocesses with stable branching

Yan Xia Ren, Renming Song, Zhenyao Sun

Research output: Contribution to journalArticle

Abstract

We consider a critical superprocess {X;Pμ} with general spatial motion and spatially dependent stable branching mechanism with lowest stable index γ0>1. We first show that, under some conditions, Pμ(|Xt|≠0) converges to 0 as t→∞ and is regularly varying with index (γ0−1)−1. Then we show that, for a large class of non-negative testing functions f, the distribution of {Xt(f);Pμ(⋅|‖Xt‖≠0)}, after appropriate rescaling, converges weakly to a positive random variable z0−1) with Laplace transform E[e−uz0−1) ]=1−(1+u−(γ0−1))−1∕(γ0−1).

Original languageEnglish (US)
JournalStochastic Processes and their Applications
DOIs
StateAccepted/In press - Jan 1 2020

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Keywords

  • Critical superprocess
  • Intrinsic ultracontractivity
  • Regular variation
  • Scaling limit
  • Stable branching

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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