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Limit theorems for a stable sausage
Stochastics and Dynamics  (IF0.98),  Pub Date : 2021-01-20, DOI: 10.1142/s0219493721500416
Wojciech Cygan, Nikola Sandrić, Stjepan Šebek

In this paper, we study fluctuations of the volume of a stable sausage defined via a $d$-dimensional rotationally invariant $α$-stable process. As the main results, we establish a functional central limit theorem (in the case when $d/α>3/2$) 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 $d/α>9/5$).