CLT for the capacity of the range of stable random walks

Wojciech Cygan, Nikola Sandrić, Stjepan Sebek

Research output: Contribution to journalArticleResearch

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

Fingerprint

Random walk
Limit Behavior
Central limit theorem
Range of data
Theorem
Class

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

CLT for the capacity of the range of stable random walks. / Cygan, Wojciech; Sandrić, Nikola; Sebek, Stjepan.

In: arXiv.org e-Print archive, 2019.

Research output: Contribution to journalArticleResearch

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