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

作　　者：Yan Xia REN Ren Ming SONG Zhen Yao SUN Jian Jie ZHAO 

机构地区：[1]LMAM School of Mathematical Sciences&Center for Statistical Science,Peking University,Beijing,100871,P.R.China [2]Department of Mathematics,University of Illinois at Urbana-Champaign,Urbana,IL,61801,USA [3]School of Mathematics and Statistics,Wuhan University,Wuhan,430072,P.R.China [4]The Faculty of Industrial Engineering and Management,Technion,Haifa,3200003,Israel [5]School of Mathematical Sciences,Peking University,Beijing,100871,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2022年第3期487-498,共12页数学学报（英文版）

基　　金：supported in part by NSFC(Grant Nos.11731009 and 12071011);the National Key R&D Program of China(Grant No.2020YFA0712900);supported in part by Simons Foundation(#429343,Renming Song)。

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(X_(t))t≥0 with branching mechanisms of infinite second moments.In the aforementioned paper,we proved stable central limit theorems for X_(t)(f)for some functions f of polynomial growth in three different regimes.However,we were not able to prove central limit theorems for X_(t)(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 X_(t)(f)for all functions f of polynomial growth.

关 键 词：SUPERPROCESSES Ornstein–Uhlenbeck processes stable distribution central limit theorem law of large numbers branching rate regime 

分 类 号：O211.4[理学—概率论与数理统计]