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Many transport processes in nature exhibit anomalous diffusive propertieswith non-trivial scaling of the mean square displacement, e.g., diffusion ofcells or of biomolecules inside the cell nucleus, where typically a crossoverbetween different scaling regimes appears over time. Here, we investigate aclass of anomalous diffusion processes that is able to capture such complexdynamics by virtue of a general waiting time distribution. We obtain a completecharacterization of such generalized anomalous processes, including theirfunctionals and multi-point structure, using a representation in terms of anormal diffusive process plus a stochastic time change. In particular, wederive analytical closed form expressions for the two-point correlationfunctions, which can be readily compared with experimental data.

Anomalous processes with general waiting times: functionals and multi-point structure