Random covering sets in metric space with exponentially mixing property

Zhang-nan Hu and Bing Li

Statistics & Probability Letters, 2021, vol. 168, issue C

Abstract: Let {B(ξn,rn)}n≥1 be a sequence of random balls whose centers {ξn}n≥1 is a stationary process, and {rn}n≥1 is a sequence of positive numbers decreasing to 0. Our object is the random covering set E=lim supn→∞B(ξn,rn), that is, the points covered by B(ξn,rn) infinitely often. The sizes of E are investigated from the viewpoint of measure, dimension and topology.

Keywords: Random covering sets; Exponentially mixing; Dynamical system; Metric space; Huasdorff dimension (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spl.2020.108922

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