Asymptotic behavior of semistable L\'evy exponents and applications to   fractal path properties
  This paper proves sharp bounds on the tails of the L\'evy exponent of an operator semistable law on $\mathbb R^d$. These bounds are then applied to explicitly compute the Hausdorff and packing dimensions of the range, graph, and other random sets describing the sample paths of the corresponding operator semi-selfsimilar L\'evy processes. The proofs are elementary, using only the properties of the L\'evy exponent, and certain index formulae. 
Peter Kern, Mark M. Meerschaert and Yimin Xiao
math.PR