Limit theorems for a stable sausage

2020/01/28 by Cygan, Wojciech, Sandrić, Nikola, Šebek, Stjepan
#60F05 #60F17 #60G52 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2001.10453

Abstract

In this article, 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).

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