TY - JOUR
T1 - Stable Central Limit Theorems for Super Ornstein-Uhlenbeck Processes, II
AU - Ren, Yan Xia
AU - Song, Ren Ming
AU - Sun, Zhen Yao
AU - Zhao, Jian Jie
N1 - Funding Information:
Yan Xia Ren is supported in part by NSFC (Grant Nos. 11731009 and 12071011) and the National Key R&D Program of China (Grant No. 2020YFA0712900). Renming Song is supported in part by Simons Foundation (#429343, Renming Song) Acknowledgements
Publisher Copyright:
© 2022, Springer-Verlag GmbH Germany & The Editorial Office of AMS.
PY - 2022/3
Y1 - 2022/3
N2 - 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.
AB - 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.
KW - 60F05
KW - 60J68
KW - Ornstein-Uhlenbeck processes
KW - Superprocesses
KW - branching rate regime
KW - central limit theorem
KW - law of large numbers
KW - stable distribution
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U2 - 10.1007/s10114-022-0559-y
DO - 10.1007/s10114-022-0559-y
M3 - Article
AN - SCOPUS:85126770903
VL - 38
SP - 487
EP - 498
JO - Acta Mathematica Sinica, English Series
JF - Acta Mathematica Sinica, English Series
SN - 1439-8516
IS - 3
ER -