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.