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

25 Sep 2020  ·  Ren Yan-Xia, Song Renming, Sun Zhenyao, Zhao Jianjie ·

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 $(X_t)_{t\geq 0}$ with branching mechanisms of infinite second moment. 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 limit 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. read more

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Probability