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On The Hitting Probabilities Of Limsup Random Fractals

Author

Listed:
  • 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)

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.

Suggested Citation

  • Zhang-Nan Hu & Wen-Chiao Cheng & Bing Li, 2022. "On The Hitting Probabilities Of Limsup Random Fractals," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(03), pages 1-9, May.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:03:n:s0218348x22500554
    DOI: 10.1142/S0218348X22500554
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