ON THE HITTING PROBABILITIES OF LIMSUP RANDOM FRACTALS

Zhang-Nan Hu (), Wen-Chiao Cheng () and Bing Li
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Zhang-Nan Hu: School of Mathematics, South China University of Technology, Guangzhou 510641, P. R. China
Wen-Chiao Cheng: ��Department of Applied Mathematics, Chinese Culture University, Yangmingshan, Taipei, Taiwan
Bing Li: School of Mathematics, South China University of Technology, Guangzhou 510641, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 03, 1-9

Abstract: Let A be a limsup random fractal with indices γ1,γ2 and δ on [0, 1]d. We determine the hitting probability ℙ(A ∩ G) for any analytic set G with the condition (⋆): dimH(G) > γ2 + δ, where dimH denotes the Hausdorff dimension. This extends the correspondence of Khoshnevisan et al.1 by relaxing the condition that the probability Pn of choosing each dyadic hyper-cube is homogeneous and limn→∞log2Pn n exists. We also present some counterexamples to show the Hausdorff dimension in condition (⋆) cannot be replaced by the packing dimension.

Keywords: Limsup Random Fractals; Hitting Probability; Hausdorff Dimension (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22500554

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