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Hausdorff and Packing Measures of the Level Sets of Iterated Brownian Motion

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  • Yueyun Hu

    (Université Paris VI)

Abstract

Burdzy and Khoshnevisan(9) have shown that the Hausdorff dimension of the level sets of an iterated Brownian motion (IBM) is equal to 3/4. In this paper, the exact Hausdorff measure function and the packing measure of the levels set of IBM are given. Our approach relies on some accurate analysis on the local asymptotic of local times.

Suggested Citation

  • Yueyun Hu, 1999. "Hausdorff and Packing Measures of the Level Sets of Iterated Brownian Motion," Journal of Theoretical Probability, Springer, vol. 12(2), pages 313-346, April.
    • Handle: RePEc:spr:jotpro:v:12:y:1999:i:2:d:10.1023_a:1021669809625
    DOI: 10.1023/A:1021669809625
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    References listed on IDEAS

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    1. Hu, Y. & Shi, Z., 1995. "The Csörgo-Révész modulus of non-differentiability of iterated Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 58(2), pages 267-279, August.
    2. Yimin Xiao, 1998. "Local Times and Related Properties of Multidimensional Iterated Brownian Motion," Journal of Theoretical Probability, Springer, vol. 11(2), pages 383-408, April.
    3. Shi, Z., 1995. "Lower limits of iterated Wiener processes," Statistics & Probability Letters, Elsevier, vol. 23(3), pages 259-270, May.
    4. Bertoin, Jean, 1996. "Iterated Brownian motion and stable() subordinator," Statistics & Probability Letters, Elsevier, vol. 27(2), pages 111-114, April.
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    Cited by:

    1. Artemi Berlinkov & R. Daniel Mauldin, 2002. "Packing Measure and Dimension of Random Fractals," Journal of Theoretical Probability, Springer, vol. 15(3), pages 695-713, July.

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