For transient symmetric Levy processes we determine a uniform lower bound for the Hausdorff dimension of the range of a process on various time sets. This complements earlier work which provided a uniform upper bound. An example is provided in which both bounds are attained.
"A Uniform Lower Bound for Hausdorff Dimension for Transient Symmetric Levy Processes." Ann. Probab. 11 (3) 589 - 592, August, 1983. https://doi.org/10.1214/aop/1176993503