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arXiv · 1910.09831

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

Wojciech Cygan·Nikola Sandrić·Stjepan Šebek
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Abstract

We prove an almost sure invariance principle for the capacity and the cardinality of the range of a class of $\alpha$-stable random walks on the integer lattice $\mathbb{Z}^d$ with $d/\alpha > 5/2$, and $d/\alpha >3/2$, respectively. As a direct consequence, we conclude Khintchine's and Chung's laws of the iterated logarithm for both processes.

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Wojciech Cygan, Nikola Sandrić, Stjepan Šebek. 2019-10-22. Invariance principle for the capacity and the cardinality of the range of stable random walks. https://arxiv.org/abs/1910.09831

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