The Levy diffusion as an effect of sporadic randomness
The Levy diffusion processes are a form of non ordinary statistical mechanics resting, however, on the conventional Markov property. As a consequence of this, their dynamic derivation is possible provided that (i) a source of randomness is present in the corresponding microscopic dynamics and (ii) that the consequent process of memory erasure is properly taken into account by the theoretical treatment.
cond-mat.stat-mech↗