论文标题
超级Ornstein-Uhlenbeck过程的稳定中央限制定理，II
Stable Central Limit Theorems for Super Ornstein-Uhlenbeck Processes, II
论文作者
论文摘要
本文是我们最近的论文的延续（Eple。J.probab。24（2019），第141号），并致力于一类超临界超临界超级Ornstein-uhlenbeck的渐近行为，$（x_t）_ {x_t）_ {t \ geq 0} $具有无限第二步的分支机制。在上述论文中，我们证明了$ x_t（f）$的稳定的中央限制定理，用于某些功能的$ f $ f $多项式增长，在三种不同的制度中。但是，对于所有功能的多项式增长，我们无法证明$ x_t（f）$的中心限制定理。在本说明中，我们表明，在三种不同制度中的极限稳定随机变量是独立的，因此，对于所有功能，我们获得了$ x_t（f）$的稳定中心限制定理，用于多项式增长的所有功能$ f $。
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.
