Abstract
Several indices, such as the Blumenthal-Getoor indices, have been defined to help describe various sample path properties for Levy 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 Levy processes. However, there has yet to be found an index that precisely determines the dimension of the graph for a general Levy process. While surveying many of these results with a focus on general Levy 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 Levy process.
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