Stable central limit theorems for super Ornstein-Uhlenbeck processes. II.

DOI10.1007/S10114-022-0559-YzbMATH Open1485.60076arXiv2005.11731OpenAlexW4220742827WikidataQ113904801 ScholiaQ113904801MaRDI QIDQ2119456

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Publication date: 29 March 2022

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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 $(X_t{)}_{tgeq0}$ 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.

Full work available at URL: https://arxiv.org/abs/2005.11731

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