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

• 作者: Yan Xia REN Ren Ming SONG Zhen Yao SUN Jian Jie ZHAO
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2022,（3）
• 页码范围: 487-498
• 页数: 12页
• 语种: 英文

摘要

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.