Hausdorff measure and packing measure of the graph of dilation-stable Lévy processes

Let X = { X ( t ) , t ∈ R + } be a dilation-stable Lévy process on R d . We determine a Hausdorff measure function ϕ ( a ) such that the graph G [ 0 , 1 ] = { ( t , X ( t ) ) : 0 ⩽ t ⩽ 1 } has positive finite ϕ-measure. We also investigate the packing measure of G [ 0 , 1 ] .