CLT for the capacity of the range of stable random walks

Wojciech Cygan, Nikola Sandrić, Stjepan Sebek

Research output: Contribution to journalArticle

Abstract

In this article, we establish a central limit theorem for the capacity of the
range process for a class of d-dimensional symmetric α-stable random walks with the
index satisfying d > 5α/2. Our approach is based on controlling the limit behavior of the variance of the capacity of the range process which then allows us to apply the Lindeberg-Feller theorem.
Original languageEnglish
Number of pages18
JournalarXiv.org e-Print archive
Publication statusPublished - 2019

Keywords

  • Capacity
  • Central limit theorem
  • Strong transience
  • The range of a random walk

ASJC Scopus subject areas

  • Mathematics(all)

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