The hausdorff dimension of the sample path of a subordinator

• DOI: 10.1007/bf02760182
• Publication Date: 2007-11-25T07:41:37Z
• Authors: Joseph Horowitz
• Keywords: Subordinator; Packing dimension; Dimension function

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.