Stable Central Limit Theorems for Super Ornstein-Uhlenbeck Processes, II
Probability
2020-09-28 v2
Abstract
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 with branching mechanisms of infinite second moment. In the aforementioned paper, we proved stable central limit theorems for for some functions of polynomial growth in three different regimes. However, we were not able to prove central limit theorems for for all functions 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 for all functions of polynomial growth.
Cite
@article{arxiv.2005.11731,
title = {Stable Central Limit Theorems for Super Ornstein-Uhlenbeck Processes, II},
author = {Yan-Xia Ren and Renming Song and Zhenyao Sun and Jianjie Zhao},
journal= {arXiv preprint arXiv:2005.11731},
year = {2020}
}