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Multifractal structure of a general subordinator

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  • Hu, Xiaoyu
  • Taylor, S. James

Abstract

The object of this paper is to obtain the multifractal structure for the local time of a general Lévy process which hits points. All such local time measures can be represented as the occupation measure of a subordinator. The thick points in the spectrum were investigated in a recent paper by Marsalle (1999. Ann. Probab. 27, 150-165). In this paper we obtain the spectrum for thin points, obtaining analogues of our results (Hu and Taylor, 1997, Stochastic Process. Appl. 66, 283-299) for the stable subordinator. We obtain our precise dimension results for exceptional sets in time rather than in space.

Suggested Citation

  • Hu, Xiaoyu & Taylor, S. James, 2000. "Multifractal structure of a general subordinator," Stochastic Processes and their Applications, Elsevier, vol. 88(2), pages 245-258, August.
    • Handle: RePEc:eee:spapps:v:88:y:2000:i:2:p:245-258
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    References listed on IDEAS

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    1. Hu, Xiaoyu & Taylor, S. James, 1997. "The multifractal structure of stable occupation measure," Stochastic Processes and their Applications, Elsevier, vol. 66(2), pages 283-299, March.
    2. Shieh, Narn-Rueih & Taylor, S. James, 1998. "Logarithmic multifractal spectrum of stable occupation measure," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 249-261, July.
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    Cited by:

    1. Hyunchul Park & Yimin Xiao & Xiaochuan Yang, 2020. "Uniform Dimension Results for the Inverse Images of Symmetric Lévy Processes," Journal of Theoretical Probability, Springer, vol. 33(4), pages 2213-2232, December.
    2. Klaus Fleischmann & Leonid Mytnik & Vitali Wachtel, 2011. "Hölder Index at a Given Point for Density States of Super-α-Stable Motion of Index 1+β," Journal of Theoretical Probability, Springer, vol. 24(1), pages 66-92, March.

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