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Random Fractals Determined by Lévy Processes

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  • Jamison Wolf

    (Tufts University)

Abstract

Several indices, such as the Blumenthal–Getoor indices, have been defined to help describe various sample path properties for Lévy processes. These indices can be used to obtain bounds on the Hausdorff dimension of the range, graph, and zero set for a special subclass of Lévy processes. However, there has yet to be found an index that precisely determines the dimension of the graph for a general Lévy process. While surveying many of these results with a focus on general Lévy processes, some of the results are generalized or improved. The culmination of this synthesis is a new index that specifies the dimension of the graph of a general multidimensional Lévy process.

Suggested Citation

  • Jamison Wolf, 2010. "Random Fractals Determined by Lévy Processes," Journal of Theoretical Probability, Springer, vol. 23(4), pages 1182-1203, December.
    • Handle: RePEc:spr:jotpro:v:23:y:2010:i:4:d:10.1007_s10959-009-0224-8
    DOI: 10.1007/s10959-009-0224-8
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    References listed on IDEAS

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    1. Rimas Norvaiša & Donna Mary Salopek, 2002. "Estimating the p-Variation Index of a Sample Function: An Application to Financial Data Set," Methodology and Computing in Applied Probability, Springer, vol. 4(1), pages 27-53, March.
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