  Many transport processes in nature exhibit anomalous diffusive properties
with non-trivial scaling of the mean square displacement, e.g., diffusion of
cells or of biomolecules inside the cell nucleus, where typically a crossover
between different scaling regimes appears over time. Here, we investigate a
class of anomalous diffusion processes that is able to capture such complex
dynamics by virtue of a general waiting time distribution. We obtain a complete
characterization of such generalized anomalous processes, including their
functionals and multi-point structure, using a representation in terms of a
normal diffusive process plus a stochastic time change. In particular, we
derive analytical closed form expressions for the two-point correlation
functions, which can be readily compared with experimental data.
