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arXiv · 2001.10453

Limit theorems for a stable sausage

Wojciech Cygan·Nikola Sandrić·Stjepan Šebek
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Abstract

In this article, we study fluctuations of the volume of a stable sausage defined via a $d$-dimensional rotationally invariant $\alpha$-stable process. As the main results, we establish a functional central limit theorem (in the case when $d/\alpha>3 /2$) with a standard one-dimensional Brownian motion in the limit, and Khintchine's and Chung's laws of the iterated logarithm (in the case when $d/\alpha>9 /5$).

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Wojciech Cygan, Nikola Sandrić, Stjepan Šebek. 2020-01-28. Limit theorems for a stable sausage. https://arxiv.org/abs/2001.10453

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