Lévy Process with Substable Increments via Generalized Convolution

We describe multidimensional Lévy processes with symmetric substable increments. The best known such process is the symmetric α -stable Lévy motion with sub-Gaussian, rotationally invariant increments. We show that these processes can be treated as stable processes subordinated by the time process and also as Lévy processes associated with generalized Lévy processes in the sense of stable generalized convolution.