Displacements of randomly arrested Lévy motions

Among other observables, Nuclear Magnetic Resonance measures characteristic functions of displacements of fluid molecules. Commonly, NMR signals are interpreted by assuming Gaussian distributions for displacements. Yet, mass transport in many complex media does not satisfy this hypothesis, and sometimes memory effects are likely occuring. Motivated by such situations, we state a closed form expression for the characteristic function of displacements of Lévy motions subordinated by Compound Poisson Processes, which account for short lived memory.