2020/05/24 by Ren, Yan-Xia, Song, Renming, Sun, Zhenyao +1
#FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.2005.11731
This paper is a continuation of our recent paper (Elect. J. Probab. 24 (2019), no. 141) 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 moment. 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 limit 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.