title: Anomalous processes with general waiting times: functionals and multipoint structure.
abstract: Many transport processes in nature exhibit anomalous diffusive properties with nontrivial 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 multipoint 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.
authors.affiliation: School of Mathematical Sciences, Queen Mary, University of London, 327 Mile End Road, London E1 4NS, United Kingdom.
authors.forename: Andrea
authors.initials: A
authors.lastname: Cairoli
authors.affiliation: School of Mathematical Sciences, Queen Mary, University of London, 327 Mile End Road, London E1 4NS, United Kingdom.
authors.forename: Adrian
authors.initials: A
authors.lastname: Baule