Fractal sets determined by dilation-stable processes

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