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The multifractal structure of stable occupation measure

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  • Hu, Xiaoyu
  • Taylor, S. James

Abstract

Let X be a stable subordinator of index [alpha] and [mu] be the occupation measure of X. Denote d([mu],x) and as the lower and upper local dimensions of [mu]. We obtain that the Hausdorff dimension of the set of the points where is (2[alpha]2/[beta]) - [alpha] a.s. and the lower bound of packing dimension is 2[alpha] - [beta] a.s. if [alpha][less-than-or-equals, slant][beta][less-than-or-equals, slant]2[alpha]. When [beta] > 2[alpha], the corresponding set is empty a.s.. And for a.s. [Omega], the set of the points where is the closure of X[0,1].

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:66:y:1997:i:2:p:283-299
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    Cited by:

    1. Fan, Ai Hua & Shieh, Narn-Rueih, 2000. "Multifractal spectra of certain random Gibbs measures," Statistics & Probability Letters, Elsevier, vol. 47(1), pages 25-31, 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.
    3. Shen, Dan & Hu, Xiaoyu, 2011. "The multifractal structure of the product of two stable occupation measures," Statistics & Probability Letters, Elsevier, vol. 81(4), pages 478-488, April.
    4. 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.

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