We hereby recall only the concept of special Levy process and its generator taken from [Applebaum09].
Let be a isotropic -stable process, which has its Levy symbol, for
See Ex 3.3.8 of [App09]. By convention, the generator associated to is denoted by, replacing in
Its Levy-Khintchine representation (see Ex3.5.9 of [App09]) is
for some constant . The precise meaning of the generator is then