Stable Central Limit Theorems for Super Ornstein-Uhlenbeck Processes, II

Yan Xia Ren, Ren Ming Song, Zhen Yao Sun, Jian Jie Zhao

Research output: Contribution to journalArticlepeer-review

Abstract

This paper is a continuation of our recent paper (Electron. J. Probab., 24(141), (2019)) and is devoted to the asymptotic behavior of a class of supercritical super Ornstein-Uhlenbeck processes (Xt)t≥0 with branching mechanisms of infinite second moments. In the aforementioned paper, we proved stable central limit theorems for Xt(f) for some functions f of polynomial growth in three different regimes. However, we were not able to prove central limit theorems for Xt(f) for all functions f of polynomial growth. In this note, we show that the limiting stable random variables in the three different regimes are independent, and as a consequence, we get stable central limit theorems for Xt(f) for all functions f of polynomial growth.

Original languageEnglish (US)
Pages (from-to)487-498
Number of pages12
JournalActa Mathematica Sinica, English Series
Volume38
Issue number3
DOIs
StatePublished - Mar 2022

Keywords

  • 60F05
  • 60J68
  • Ornstein-Uhlenbeck processes
  • Superprocesses
  • branching rate regime
  • central limit theorem
  • law of large numbers
  • stable distribution

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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