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The hausdorff dimension of the sample path of a subordinator

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Abstract

The Hausdorff dimension of the range of an arbitrary subordinator is exactly determined in terms of the rate of linear drift and the Levy measure of the subordinator. This generalizes the result of Blumenthal and Getoor: that for a stable subordinator of indexσ, the dimension of the range isσ.

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References

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Authors and Affiliations

  1. University of Michigan, Ann Arbor, Michigan

    Joseph Horowitz

  2. University of Toledo, Toledo, Ohio

    Joseph Horowitz

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  1. Joseph Horowitz
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Horowitz, J. The hausdorff dimension of the sample path of a subordinator. Israel J. Math. 6, 176–182 (1968). https://doi.org/10.1007/BF02760182

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  • DOI: https://doi.org/10.1007/BF02760182

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