From Semi-Markov Random Evolutions to Scattering Transport and Superdiffusion

We here study random evolutions on Banach spaces, driven by a class of semi-Markov processes. The expectation (in the sense Bochner) such is shown to solve some abstract Cauchy problems. Further, telegraph (damped wave) equation generalized case perturbations. A special attention devoted models scattering transport processes which can be represented through these evolutions. In particular, we consider flights with infinite mean flight times turn out governed generalization linear Boltzmann equation; their scaling limit proved converge superdiffusive