Invariance principle for the capacity and the cardinality of the range of stable random walks

Wojciech Cygan, Nikola Sandrić and Stjepan Šebek

Stochastic Processes and their Applications, 2023, vol. 163, issue C, 61-84

Abstract: We prove an almost sure invariance principle for the capacity and the cardinality of the range of a class of α-stable random walks on the integer lattice Zd with d/α>5/2, and d/α>3/2, respectively. As a direct consequence, we conclude Khintchine’s and Chung’s laws of the iterated logarithm for both processes.

Keywords: Range of a random walk; Capacity; An almost sure invariance principle; Law of the iterated logarithm (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spa.2023.05.012

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