Limit theorems for a stable sausage

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Contributors

  • Wojciech Cygan - , Institute of Mathematical Stochastics, TUD Dresden University of Technology, University of Wrocław (Author)
  • Nikola Sandrić - , University of Zagreb (Author)
  • Stjepan Šebek - , Graz University of Technology, University of Zagreb (Author)

Abstract

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).

Details

Original languageEnglish
Article number2150041
JournalStochastics and Dynamics
Volume21
Issue number7
Publication statusPublished - 1 Nov 2021
Peer-reviewedYes

Keywords

ASJC Scopus subject areas

Keywords

  • Functional central limit theorem, law of the iterated logarithm, stable process, stable sausage