Random Fractals Determined by Lévy Processes

Jamison Wolf ()
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Jamison Wolf: Tufts University

Journal of Theoretical Probability, 2010, vol. 23, issue 4, 1182-1203

Abstract: 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.

Keywords: Lévy process; Hausdorff dimension; Blumenthal–Getoor indices; p-variation; 60G51; 60G17; 28A80 (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10959-009-0224-8

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